text:
      <ba-card cardTitle="Personal Details" baCardClass="with-scroll">

          Name *
          <input type="text" class="form-control" id="input01" placeholder="Name" [formControl]="name"  >

          Please enter name.

          Sex

                <input type="radio" name="sex" id="inlineRadio2" [formControl]="sex" value="M" >
                Male

                <input type="radio" name="sex" id="inlineRadio3" [formControl]="sex" value="F" >
                Female

          Age
          <input type="number" class="form-control" id="input02" placeholder="Age" [formControl]="age">

          Please enter age. It should be a number.

          Mobile No *
          <input type="text" class="form-control" id="input05" placeholder="Mobile No" [formControl]="mobile_no">

          Please enter mobile number.

          Occupation
          <input type="text" class="form-control" id="input06" placeholder="Occupation" [formControl]="occupation">

          Email ID *
          <input type="email" class="form-control" id="input07" placeholder="Email ID" [formControl]="email">

          Please enter valid email.

          Facebook ID
          <input type="text" class="form-control" id="input08" placeholder="Facebook ID" [formControl]="facebook">

          What is your fitness goal ?
          <select class="form-control" [(ngModel)]="fitness_goal">
            <option *ngFor="let fg of fitness_goals" [ngValue]="fg" >{{fg.name}}</option>
          </select>

          How do you hear about Muscle Garage ?
          <select class="form-control" [(ngModel)]="heard_from">
            <option *ngFor="let hf of heard_froms" [ngValue]="hf" >{{hf.name}}</option>
          </select>

          Did anyone reffered ?

                <input type="radio" name="refference" id="inlineRadio4" [formControl]="refference" value="1" (change)="handleChange($event)" >
                Yes

                <input type="radio" name="refference" id="inlineRadio5" [formControl]="refference" value="0" (change)="handleChange($event)">
                No

          Reffered By
          <input type="text" class="form-control" id="input09" placeholder="Reffered By" [formControl]="referred_by">

      </ba-card>

      <ba-card cardTitle="To be completed by Member of Staff" baCardClass="with-scroll">

          Co-Ordinator *
          <input type="text" class="form-control" id="input21" [formControl]="co_ordinator" placeholder="Co-Ordinator">

          Please enter Co-Ordinator.

          Conatct No *
          <input type="text" class="form-control" id="input23" [formControl]="co_ordinator_no" placeholder="Mobile No">

          Please enter mobile number.

      </ba-card>

      <ba-card cardTitle="Package Details" baCardClass="without-scroll">

              Package Suggested
              <select [(ngModel)]="membership_type" class="form-control">
                <option *ngFor="let m of memberships" [ngValue]="m">{{m.name}}</option>
              </select>

              Offered Price
              <input type="text" class="form-control" id="input37" [formControl]="amount" placeholder="Amount" />

          When can we expect

              <input class="form-control" placeholder="yyyy-mm-dd" name="dp2" [(ngModel)]="expect_at"  ngbDatepicker #d10="ngbDatepicker" value="expect_at" >

          Comments
          <textarea placeholder="Comments" class="form-control" id="textarea01" [formControl]='comments'></textarea>

      </ba-card>

        <button type="button" class="btn btn-lg btn-block" [ngClass]="{'btn-default': form.invalid, 'btn-success': form.valid}" (click)="submitData()">SUBMIT</button>


text:
Drogba sinks hat-trick in MLS start
But two typically clinical Drogba strikes just after the hour mark capped a memorable evening for the 37-year-old Ivory Coast legend, who celebrated by presenting his jersey to a fan after the match."The crowd was amazing," Drogba told reporters. "And, you know, this Man of the Match [trophy] that they gave me at the end, it's for them. I give it to them."Drogba's treble was the classic striker's full house — one goal scored with his left boot, another with his right and another from his head.It left interim Impact coach Mauro Biello purring with pleasure. "What can I say? What a performance from Didier," Biello said."He's such a committed person. He's won everywhere."He came here with a great spirit, with such a will to win. And we saw that tonight."Nevertheless Drogba was not happy with his team's display in the win."For me, it's not a good result," Drogba said. "The most important thing is that you get the three points, but when you look at the game itself, you know we've got a lot of things to change and to work on. There's always room for improvement in this team."0Shares0000(Visited 1 times, 1 visits today) 0Shares0000Montreal Impact's Didier Drogba reacts after scoring against the Chicago Fire during second half of a MLS soccer game in Montreal, Saturday, Sept. 5, 2015. PHOTO/MLSMONTREAL, September 6- Didier Drogba launched his Major League Soccer career in style here Saturday, scoring a hat-trick on his first start for new club Montreal Impact in a 4-3 win over Chicago Fire.The former Chelsea striker opened his goalscoring account on 21 minutes before Chicago battled back into the contest to take a 3-2 lead early in the second half.
oqrkbkep 上海manhattan酒吧玩法, 上海夜网WX, 上海龙凤千花, 南京桑拿温泉推荐, 夜上海论坛DS, 成都现在营业的舞厅有哪些, 杭州用口的SPA, 杭州西湖阁最新, 武汉饼子论坛, 深圳夜生活, 爱上海JW, 爱上海LG, 苏州洗浴中心水磨服务, 长沙kb老场子, 阿拉上海阿拉浦东

redpajama_set_name: RedPajamaCommonCrawl


text:
2019-2020 Executive Summary
2020-2021 Judicial Hellhole Report
Philadelphia Court of Common Pleas & the Supreme Court of Pennsylvania
South Carolina Asbestos Litigation
The City of St. Louis, Missouri
Cook, Madison & St. Clair Counties, Illinois
05.11.2012	Points of Light
New Jersey Protects 'Good Samaritans' Trying to Save Lives
New Jersey Gov. Chris Christie has signed into law a refreshingly bipartisan act by the state legislature that will protect good samaritans who use portable defibrillators to try to save the lives of sudden heart attack victims.
As reported by NJToday.net, the "law, S-852, eliminates language in state statute that requires a person using an automated external defibrillator (AED) to have received training in both CPR and the usage of the AED. The law reduces requirements that entities require CPR and AED training for all people who might use the AED to just the people most likely to use the device."
More importantly, it "provides immunity from civil liability to any lay person who uses an AED and fails, in good faith, to request emergency medical assistance as soon as practical. It also provides immunity to the organization that has acquired the AED. AEDs are designed to walk someone who may never have used the device through the steps to safely perform the defibrillation process. Current devices speak the instructions, step-by-step, and will only administer a defibrillation if the victim needs it."
Roughly 300,000 people in the U.S. suffer sudden cardiac arrest each year, and health experts say there is a 90 percent chance of survival if defibrillation is performed within the first minute of the crisis.
Tags: defibrillation, good samaritans, Gov. Chris Christie, New Jersey, sudden heart attacks
Missouri Judiciary Needs to Address Efficiency Concerns
Activity in state legislatures across the country is starting to ramp up as legislators look to tackle a variety of
Judicial Hellholes
Op-Ed: Courts in 'Judicial Hellholes' Less Likely to Abide by SCOTUS Precedent
There is a growing trend across the nation of state courts in "Judicial Hellholes" rejecting U.S. Supreme Court precedent and
Op-Ed: COVID-19 Lawsuits Ravage Businesses
This piece was originally published by the Washington Times. For those across the country who fear potential lawsuits in the
Since its inception in 2002, the American Tort Reform Foundation's Judicial Hellholes® program has documented in annually published reports various abuses within the civil justice system, focusing primarily on jurisdictions where courts have been radically out of balance.
To receive new posts automatically via e-mail, enter your name and email address:
Hellhole News
© 2021 Judicial Hellholes.


The best way to start saving on your electricity costs is to get smart with how you use electricity. In an average home, the computers, laptops and printers etc account for around 5% of the Electrical Bill.
However, with a few simple changes you can make sure that your Business system doesn't cost the earth. Here are our top Six energy-saving tips for your Computers laptops and printers.
It's not just your TV that uses a lot of energy though. Your computer and laptop can be just as energy-draining if not used correctly.
The easiest choice to make is between a desktop and computer monitor or a much smaller laptop. A laptop is more energy-efficient than a desktop and monitor set-up.
Laptops, desktops, and monitors are becoming increasingly energy-efficient, especially when you compare LCD or LED monitors with the old-style tube or CRT monitors. So again, if you have an older model it might be worth thinking about upgrading to a newer, energy-efficient model.
Newer machines also have reasonably good power options, so they switch on and power down fairly quickly, making it less tempting to just leave your computer on unnecessarily. This is a sure fire way to waste energy. You're far better off simply turning your laptop off when not in use.
Use your power-saving setting: these are usually found in your computer preferences, and there are normally two options, either sleep or hibernate mode, both will turn off the monitor within a specified number of minutes of inactivity – with an old tube/CRT monitor energy usage may fall by half.
Don't forget to switch off your computer and any peripheral devices, such as your printer and scanner, overnight. Check your back-up settings and make sure it is set up to run as soon as your computer is switched on again (in case your computer is switched off at the designated time).
Energy-saving tips for your Printer.
The Energy Star label on the printer is a badge of honor for energy efficiency. American businesses and families have saved 430 billion dollarson their energy bills since Energy Star was established in 1992. If your printer has energy star qualifications, it has passed rigorous testing for quality, efficiency, and environmental safety.
This feature is guaranteed to lower your electricity bills. Sleep mode or automatic shut off put your printer in a reduced power state if idle for a specified period of time.
Using your printer's Draft mode cuts print times and reduces the amount of power your printer consumes – as well as helping you to make some serious savings on the amount of ink or toner you use. Enable it for all internal correspondence, where presentation isn't a major issue.
Choose devices that feature 'instant on' technology, so that you're not left waiting around each time your device comes out of sleep mode. With quicker time to start-up, these devices consume less power – making it more likely that you'll switch them off when not in use.


If you're hoping to buy a desirable business for sale, chances are good you're not the only one. Here's how to stand out from the crowd and snag the sale.
Once you've chosen a business you're interested in buying, your next task is developing an offer and making your interest known to the current owner.
In some cases, this phase of the business-buying process can be likened to attending a job interview. If there are multiple buyers, all vying for the opportunity to put in their offer, it can be daunting. You'll want to put your best foot forward, of course, and make sure you're not overlooked. But, at the same time, you need to keep your head in the game and make sure you don't get so caught up in the competitive aspect of the situation that you end up making an unwise decision you'll regret down the road.
If you've selected this business based, at least in part, on your personal experience, knowledge base, and skill level, you should be able to rely on these to bolster your confidence heading into the inquiry stage.
Again, like a job interview, how you carry yourself says a lot about the kind of owner you're likely to be. Most business owners care about what's going to happen with their company after they leave, even if they need to sell quickly. If you can impress the seller with what you can do and how your skills will support his or her business going forward, you should be able to convince them you're the best buyer for their business.
Show them that you've done your research and don't be afraid to ask questions. Prove that you're a determined to succeed and committed to offering the best deal possible for both parties. Sometimes, the difference between winning and losing a bid for a business is simply staying at the top of the seller's mind.
While the value of the business you've chosen, and the eventual offer you make, are both important to both you and the seller, many buyers make the mistake of considering it the only item of importance in the transaction. As noted above, most sellers are heavily emotionally invested in their businesses. They're not just robots waiting for the right financial lever to be pulled.
Showing that your interest in the company goes beyond strictly financial matters can quickly set you apart from those prospective buyers whose outlook is limited in that respect.
From a purely practical standpoint, it's both irritating and frustrating to a seller when prospective buyers waste their time by responding to advertisements or businesses for sale listings without reading it thoroughly. They ask questions the ad already answers, provide information the seller doesn't want or need, and generally end up sounding disengaged or worse.
If you want to stand out positively, it is crucial that you thoroughly review the ad or listing, responding to each feature appropriately with your own information or an intelligent question or two. Go into as much detail as you can in areas where the current owner is seeking feedback to show you care about their vision for the new owner of their business. Sellers can only appreciate a buyer who makes the effort to address their points and strives to meet their expectations.
In summary, the real key to standing out as a prospective buyer is to recognize the fact that the seller has undoubtedly put a lot of work into the business over the years. They want to know that the company they may consider as their personal legacy will be in the best possible hands going forward. Pretend you are the seller and think about what you would want from a potential buyer, then try to be that buyer.


Size range is 54mm, cast in pewter, painted by experienced Irish artists, designed by Chris Tubb, internationally famous designer. Also available separately - Drummer, Standard Bearer, Foot Soldier.
Click the button below to add the 54mm scale Irish Brigade Union Army Officer pewter figure to your wish list.


text:
Dwayne Johnson Gets Emotional Talking About First Time Working Out With Father
Dwayne Johnson Recalls His First Ever Workout With His Dad
byDerek Hall
Photo via Instagram @therock
Dwayne Johnson is one of the biggest stars in Hollywood, both figuratively and literally. Now the action star and WWE legend shares the story of his first time working out.
Johnson comes from a family of wrestlers. Even though he has since ventured into other fields, that part of his lineage is still very important to him. After all, it was the first time the world was introduced to the massive athlete he is.
A post shared by therock (@therock)
Dwayne Johnson got most of his influences from his father, the late Rocky Johnson. He followed into his father's footsteps by wrestling, and as he explained in a recent Q&A session, his father is the whole reason he started working out in the first place. He recounted the story when asked about his first time training.
"I first started working out when I was 12 years old," says Johnson. "I had my first official workout with my dad, Rocky Johnson, rest in peace old man, he passed away January 15th of this year.
"My dad was a workout beast and animal and he was built like a brick house," Johnson continued. "I would always go to the gym with my dad and watch him on the weekends, but I wasn't allowed to work out. So I'd just watch him and all his OG buddies in the gym, hard training and clang-and-bang, those old school dudes.
"So 12 years old in Hawaii, my dad finally said, 'Alright you can come to the gym with me,' and it was a Saturday so I was really pumped to go to the gym with my dad. Before we walked in he said 'Listen. You're gonna work your a– off. I don't want any bulls–t.' He goes, 'Whatever you put on the bar, when we do bench press, I'm going to show you how to do bench press first, whatever we put on the bar you have got to push it up. Whatever weight you choose, you've got to push it up, you've got to get it out of the hole."
Johnson went on to detail starting with 25lb on each side. Then they increased it to 35lb, which he barely was able to push. Despite his dad's hesitation, Dwayne insisted on increasing the weight to 45lb.
"I'm feeling myself at 12 years old, I don't know why by the way because I had a f—ed up afro and acne all over the place, but I was still feeling myself."
So Dwayne Johnson tried to push the weight, but it got stuck on his chest. Ultimately it was too heavy, and he could not lift it off. He was ultra embarrassed, and his dad would not help him. Finally getting the weight off to the side, he got up angry but his dad gave him some solid advice.
"He said, 'Don't worry about other people looking at you, don't ego train. Don't ever train for your ego. It doesn't matter. Who gives a s–t who's watching you? You train for results and you train with weight that you can control.' That's how you're gonna be a master, basically, in the gym, is what he was trying to say."
This is a sage piece of advice that Dwayne Johnson got from his father. Ego training is not good for anybody, and can even hurt people.
Categories: Entertainment News Videos
Tags: CelebrityDwayne JohnsonThe Rock
Blessing Awodibu Shares The Most Hilarious Home Workout Video Ever!
12 Strongest Bodybuilders Of All Time
Derek Hall
Staff News Writer and interviewer for MMA, powerlifting, bodybuilding, strongman, and CrossFit. Full time fight fan, part time participant. Bringing out of the box thinking to the world since 1995. Opinions are strictly my own.
'Remember The Titans' Actor Ethan Suplee Reached His Abs Goal After Dramatic Weight Loss
Busta Rhymes Shares Secret To His 100lb Weight Loss Transformation
Kumail Nanjiani Body Shamed, Accused Of Steroid Use Following Transformation
Watch: Thor Actor Chris Hemsworth Unleashes Hammer Fists During Mitt Drills
Dwayne Johnson Needed Stitches After Bloody Training Session, Licks His Own Blood!
Chris Cuomo's Fake Weight Controversy, Joe Rogan Admits He Was Wrong
Blessing Awodibu Is A Shredded 287lb As He Begins Prep For Pro Debut


text:
Q: Initializer does not override a designated initializer from its superclass, Swift 2.0 Working thru this appcoder tutorial building a text to speech app tutorial and run into a swift 1.2-> swift 2.0 feature.
The demo project has a class in it... which the Xcode 7.1.1 under IOS 10.11.1 doesn't like, giving me the error. "initialiser doesn't override the designated initialiser from its super class" on the override init() statement, followed by the error "Must call the designated initialiser of the superclass UISlider".
Ok, Rather new to Swift; and quite where I start to fix this is a little lost on me.
class CustomSlider: UISlider {

var sliderIdentifier: Int!

override init() { <--- error here
    super.init()  <--- error here

    sliderIdentifier = 0
}

required init?(coder aDecoder: NSCoder) {
    super.init(coder: aDecoder)

    sliderIdentifier = 0
}

}

What should this code snippet say?

A: Since UISlider doesn't define or inherit init() as a designated initializer, you can't call it from your subclass init.
class CustomSlider: UISlider {

    var sliderIdentifier: Int!

    required init() {
        super.init(frame: CGRect.zero)
        sliderIdentifier = 0
    }

    required init?(coder aDecoder: NSCoder) {
        super.init(coder: aDecoder)
        sliderIdentifier = 0
    }

}

In this case, you could factor out the initialization of sliderIdentifier and just inherit all of UISliders initializers:
class CustomSlider: UISlider {

    var sliderIdentifier: Int! = 0

}

For more information, read the section titled "Designated Initializers and Convenience Initializers" in The Swift Programming Language.

redpajama_set_name: RedPajamaStackExchange


Laughlin has something for everyone to enjoy. Nearly 2 million visitors a year come to Laughlin to take advantage of world-class performers, great food and good times. Casino action, boating, fishing, hiking, off-road racing, and more. Come find out what the best-kept secret this side of the Colorado River is all about. Major Events include the Annual Laughlin Biker River Run, celebrating 35 straight years in 2017. Only 5 miles away is the 70 mile long Lake Mohave with hundreds of secluded coves.


text:
Home What's On Following Audre Lorde's path
Following Audre Lorde's path
by Dani Arbid
We all leave our footprints on the cities we grace. When you're Audre Lorde, the 20th century's most famous African American lesbian activist, your footprint leaves a longer trace. Follow the feminist writer's last years in a new self-guided interactive tour, "Audre Lorde - The Berlin Years 1984 to 1992." All you need is a smartphone, a data plan and then navigate to the mobile website. Once you've made it to a specific location, open the respective pin and get a handful of information, photos and sometimes soundclips about what the significance of the location was to Audre Lorde. No tour guide necessary, no tipping! The excursion boasts 38 locations, from the lakeside retreat of the Wannseeterrassen, which Audre often liked to frequent with her partner Dr. Gloria I. Joseph and friend and collaborator Dagmar Schultz (who also spearheaded this tour concept), to the main building of the Technical University, where Audre gave a seminal reading in 1984. Visit the Haus der Kulturen der Welt, where Audre delivered her provocative talk in 1988, which appeared in the book Power and Sensuality, alongside Adrienne Rich. Or, try the former Café April in Kreuzberg, now the vegetarian/vegan Cafe V, where Audre convinced the writer Ika Hügel-Marshall to write a book about her – which she eventually did.
Audre Lorde - The Berlin Years 1984 to 1992
Books Tours literature Feminism


The latest figures for drug-related deaths in Scotland were released this month and they don't make for good reading. According to statistics released by National Records Scotland, a total of 934 deaths were registered in 2017. This represents an 8% increase on the previous year and more than double the figure for 2007, which was 455.
As was the case in previous years, problem drug use associated with the use of opiates or opioids (e.g. heroin, morphine and methadone) are the leading cause of these deaths. These drugs were implicated in, or potentially contributed to 87% (815) of the deaths recorded in 2017.
The 934 deaths in 2017 is the highest ever recorded and marks the fourth consecutive year in which the total number of deaths has risen. Over the last decade the number of deaths has increased by 105%. During this time the average number of deaths per year was 687, just under double than in the previous decade from 1997-2007 (average of 366 deaths). Although men still account for the majority of deaths, a recent report by the Scottish Government highlights an increase in the proportion of deaths among women from 19% in 2002-2006 to 29% in 2012-2016.
Why do drug-related deaths keep increasing?
The underlying causes of drug-related deaths are complex and there is no consensus on why they have increased steadily over the last decade in Scotland. A number of contributing factors have been suggested.
The chart below shows how the proportion of people over the age of 35 dying because of drug misuse has increased dramatically over the last decade. The figures show that the highest number of drug-related deaths in 2017 was among people aged 35-44.
The 2008 financial crisis has resulted in the pursuit of austerity policies and welfare reform. A report by the Advisory Council on the Misuse of Drugs, published in 2016, states that areas that experience the highest rates of drug-related deaths are among those that have experienced the greatest reductions in funding for local authority services and welfare benefits for working age adults.
The link between drug-related deaths and deprivation is also reflected in geographical data. Health boards with the highest average annual number of drug related deaths such as Greater Glasgow and Clyde, Tayside and Lothian encompass the cities of Glasgow, Dundee and Edinburgh where the largest areas of concentrated deprivation in Scotland occur.
Despite the reduction in funding for ADPs, national performance against the waiting time target for drug services has been exceeded, although there is variation across the country. For example, 79.9% of clients seeking help in Lothian were seen within 3 weeks. The target is 90%.
The national drug strategy – a fresh approach?
The full debate can be viewed in the video below.
Recent reaction to the latest drug-related death statistics in the media has prompted calls for a cross-party approach to develop the revised strategy. The extent to which the Parliament is involved in shaping this will become clearer in the run up to its expected publication later this year.
A more detailed overview of some of the issues covered in this blog can be found in SPICe's briefing on drug misuse.
Previous Post: International Bog Day 2018: Where are we with the restoration of Scotland's Bogs?


text:
O'Flaherty Heim Birnbaum Kirchner & Curtis Ltd. > Business & Real Estate Law > Long Saga Of Wrongfully Terminated Attorney Continues
Long Saga Of Wrongfully Terminated Attorney Continues
Even Attorneys can be unlawfully terminated. In this case, an arbitration panel found that Menards had wrongfully terminated Dawn Sands, their executive general counsel, as retaliation for her assertion for equal pay to her male counterparts under Title VII of the Civil Rights Act of 1964. In 2007, an arbitration panel awarded Ms. Sands over 1.4 million in back pay, liquidated damages, compensatory damages and punitive damages as well as $129,120.25 in attorney fees. In a surprise twist, they also ordered her reinstatement. Menards appealed and the Court of Appeals affirmed, Menards appealed again and the Supreme Court overturned the reinstatement but remanded for an award of front pay in order to make Ms. Sands "whole."
For the second time, the parties have again appealed to the Court of Appeals. The Circuit Court awarded Ms. Sands a front pay award of $603,333 and $576,469 in attorney fees. On remand, the Circuit Court refused to hear any evidence on the issue of front pay. The Circuit Court also refused to hear Menard's two §806.07(1)(h) motions. Menards motions were based on after-acquired evidence of misconduct and evidence that Ms. Sands had paid her sister for false testimony during the arbitration proceedings. Menards also appealed the attorney fees award. The Court of Appeals ultimately found that dismissal of the first motion was proper given that Sand's back pay award ended long before Menard's found her misconduct, therefore Menards would not have been entitled to disgorgement as a matter of law. The Court of Appeals did remand Menard's second motion back to the Circuit Court on whether Sands paid her sister for testimony at the arbitration proceeding, saying that such issue goes to the integrity of the arbitration proceedings themselves. In the interest of judicial efficiency, the Court then considered if the circuit court denied that motion, whether an evidentiary hearing should be held on the issue of front pay.
Both parties sought to introduce evidence on front pay, Ms. Sands sought to introduce evidence that she intended to remain with Menards for her entire career and Menards that Sands requested only two years of front pay at her arbitration hearing thereby judicially estopping her from receiving more and that Ms. Sands had failed to mitigate her damages. The Court of Appeals ultimately found that nothing barred Ms. Sands from her ability to introduce evidence of her intention to remain employed with Menards until retirement. Further, they found that she was not judicially estopped from receiving only 2 years of front pay as a result of her testimony at the arbitration proceeding. As rationale the court noted that because Ms. Sands failed to convince the arbitration panel of her position, the third element of estoppel was missing and more importantly at the time she requested it, she would not have foreseen the arbitration panel awarding reinstatement and that Menards would put up a lengthy and very public refusal to comply, which ultimately may have damaged Ms. Sands career possibilities.
Menards also argues Ms. Sands is barred from receiving front pay for failure to mitigate her damages. The Court of Appeals again disagreed, stating that while she did decline a job offer in October 2006, the arbitrators still elected to reinstate her. From the time the arbitration award was given until the Supreme Court overturned the reinstatement, Ms. Sands would not have had a duty to mitigate her damages. However, the Supreme Court case ended over two years ago, and the Court of Appeals did find that Menards should be able to present evidence of her failure to mitigate damages since the Supreme Court ruling. The Court of Appeals also found that Menards should have been allowed to present its after-acquired evidence with respect to the determination of front pay, but also found that such evidence would not have barred her from recovering. The Court of Appeals found that an award of front pay would have begun in 2007 had reinstatement not been ordered, and that the after-acquired evidence was not discovered until late 2010. Therefore, at best, Ms. Sands front pay award could be limited by the after-acquired evidence to the time period between 2007 and late 2010.
The last issue before the Court of Appeals was whether the Circuit Courts award of $576,469 in attorney fees was appropriate. Sands had petitioned the court for $671,062.38 in attorney fees, which she claimed represented her fees since the day of the arbitration decision. Menards opposed the fees saying she could not recover because she was not a prevailing party and that her fee petition was insufficient. The Court of Appeals found that even though Menards had appealed to the Supreme Court, Ms. Sands had prevailed in that the Supreme Court had awarded her front pay in lieu of reinstatement in order to make her whole, making her a prevailing party for purposes of the attorney fees award. The Court of Appeals did find however that her fee petition was insufficient. The Circuit Court with little rationale had rejected Ms. Sands fee request, saying it was borderline shocking to the conscience but then awarded her the amount Menards had spent on attorney fees. In doing so it did not determine the reasonableness of her attorney fees petition, including whether the hourly billing rate was reasonable and if it was true that Ms. Sands' attorneys had included numerous entries for legal work for Ms. Sand's sister as Menards purported.
There are many significant issues standing between Ms. Sands and her award for front pay, including Menard's motion on the issue of whether Ms. Sand's paid her sister for testimony at the original 2007 arbitration proceeding, failure to mitigate her damages and the after acquired evidence of her misconduct if considered. Given the numerous issues again remanded to the circuit court, whether this is the last trip to the Court of Appeals for Menards and Ms. Sands remains to be unseen.


text:
Justia Patents US Patent for Measurement of topography using polarimetric synthetic aperture radar (SAR) Patent (Patent # 5,552,787)
Measurement of topography using polarimetric synthetic aperture radar (SAR)
Oct 10, 1995 - The United States of America as represented by the Secretary of the Navy
The polarimetric technique of measuring azimuth direction terrain slopes utilizes a polarimetric synthetic aperture radar (SAR) to provide a direct measure of terrain azimuthal slopes and a derived estimate of terrain elevation. Utilizing this measure of the azimuthal slopes and estimated terrain elevations, a one-dimensional terrain slope map over a wide area may be produced without any prior knowledge of the terrain. Utilizing the method of steepest descent (or gradients) the polarimetric orientation of the peak (maximum) of the signature is determined for each image pixel. The terrain elevations are derived by integrating the slopes in the azimuthal direction and may be further refined so as to obtain absolute, rather than relative, elevation values by independently knowing at least one elevation "tie-point" along each slope profile being integrated. These orientations are proportional to terrain slope in the azimuthal direction. Processing of all the image pixels allows a complete two-dimensional topography elevation map of the terrain slopes can then be constructed from sets of elevation profiles spaced throughout the range direction.
Latest The United States of America as represented by the Secretary of the Navy Patents:
Real-Time Automation for Monitor and Control of Electro-Mechanical System
Highly Stable Semiconductor Lasers and Sensors for III-V and Silicon Photonic Integrated Circuits
Optical Waveguide
Transmission security method using bounded arbitrary frequency modulation
Systems and methods to relocate live compute assets
This invention pertains generally to topographic mapping and more specifically to the measurement of topography over a wide area utilizing a polarimetric synthetic aperture radar (SAR) installed in an aircraft or satellite.
Wide-area measurements of topography currently utilize either stereo-photography or interferometric synthetic aperture radar (IFSAR). However, stereo-photography is limited by the weather, atmosphere (absorption, refraction, turbulence, etc.) and darkness.
Microwave interferometric SAR has shown promise as a wide-area technique for the measurement of topography but has its own set of limitations. Radar mapping utilizing interferometric principles was first applied in the late 1960's and early 1970's to earth-based observations of Venus and the moon. The simultaneous measurement of range, azimuth angle, and elevation angle provides the absolute three-dimensional location of each image point, thus radar images can be accurately transformed from slant range to ground range format. This enables the correction of radar artifacts such as foreshortening and simplifies the coregistration of diverse images. The combination of one interferometric channel with simultaneously operated channels (multifrequency, multipolarization) will permit automatic generation of multichannel three-dimensional geolocated radar images. The interferometric technique utilizes the property that a small time delay difference is associated with a phase shift. Phase measurements made by interferometric SAR provide the opportunity for accurate elevation measurements, however, a different set of measurement problems are created. The major phase measurement problems involve (1) exact knowledge of the scattering path geometry, (2) platform motion compensation, and (3) 2.pi. phase ambiguities caused by abrupt elevation changes which require "unwrapping" algorithms and constitute recovering the multiples of 2.pi. phase differences that "disappear" in an interferogram. See, Madsen et al., Analysis and Evaluation of the NASA/JPL TOPSAR Across-Track Interferometric SAR System, IEEE Trans. Geosc. and Remote Sensing, Vol. 33, No. 4, pp. 383-391, 1995; E. Rodriguez et al., Theory and Design of Interferometric Synthetic Aperture Radars, IEEE Proc.-F, Vol. 139, No. 2, pp. 147-159, 1992; Li et al., Studies of Multibaseline Spaceborne Interferometric Synthetic Aperture Radars, IEEE Trans. Geosc. and Remote Sensing, Vol. 28, No. 1, pp. 88-97, 1990; and U.S. Pat. No. 4,975,704, Gabriel et al.
Forest areas present additional problems for interferometric SAR since practical antenna baseline separations for aircraft and single satellite applications generally imply the use of microwave frequencies too high to penetrate forest canopy to the ground. Polarimetric SAR at the P-band and lower frequencies provide a method for the measurement of topography in forested areas and may be used as a measurement tool which can aid in solving the phase ambiguity problems of interferometric SAR. Polarimetric SAR slope and elevation measurements can provide bounds on the IFSAR phase path. Finally, the relative simplicity of fully-polarimetric real, and synthetic aperture, radar design has resulted in a rapid expansion in the number of such systems, application and datasets. Many of these datasets involve geophysical parameter measurements which may utilize the techniques taught by this invention to improve the estimate of the parameter.
The object of this invention is to provide a method and apparatus for the direct measure of terrain azimuthal slopes so as to derive an estimate of terrain elevation.
Another object of this invention is to provide an apparatus and method having low rms error values and high correlation values that is capable of providing topographic information over a wide area so that geophysical parameters, when such information is needed to correct radar studies of as soil moisture, biomass density, and crop type may be accurately measured by radar.
These and other objectives are attained by measuring the full amplitude of a phase scattering matrix obtained by measuring the orthogonal components, vertical and horizonal, of electromagnetic reflections of a synthetic aperture radar (SAR). These orthogonal components are analyzed in phase and amplitude to obtain a polarimetric signature of the terrain through the use of a scattering matrix of the electromagnetic reflections. Utilizing the method of steepest descent (or gradients) the polarimetric orientation of the peak (maximum) of the signature is determined for each image pixel. These orientations are proportional to terrain slope in the azimuthal direction. Processing of all the image pixels allows a map of the terrain slopes to be generated.
FIG. 1 shows the source of the Stokes-Mueller matrix data and its structure.
FIG. 2 shows the Stokes vector processor module.
FIG. 3 shows the flow diagram for the generation of a topographic slope map from measured polarimetric data.
FIG. 4 shows the process for generation of a polarimetric signature from uncompressed, averaged Stokes-Mueller matrix data.
FIG. 5 shows the flow diagram for the generation of a topographic slope or elevation map from measured polarimetric data.
FIG. 6 shows the slope to elevation processor.
FIG. 7 shows the apparatus for acquiring polarimetric data and processing such data to a three-dimensional topographic map.
FIG. 8 shows the topography of the Breg River valley topography.
FIG. 9a shows the terrain azimuthal slope profile comparison between those shown on the digital-elevation map (DEM) and those obtained by the polarimetric synthetic aperture radar (SAR) on a azimuthal transect of the Breg River valley at a range of 300 meters.
FIG. 9b shows an estimate of the terrain elevation profile on a directional transect of the Breg River valley at a range of 300 meters.
FIGS. 10a shows the terrain azimuthal slope profile comparison between those shown on the digital-elevation map (DEM) and those obtained by the polarimetric synthetic aperture radar (SAR) on a azimuthal transect of the Breg River valley at a range of range of 700 meters involving more complex terrain slopes.
FIG. 10b shows the terrain elevation profile on a directional transect of the Breg River valley at a range of 700 meters.
FIG. 11a shows the terrain azimuthal slope profile comparison between those shown on the digital-elevation map (DEM) and those obtained by the polarimetric synthetic aperture radar (SAR) on a azimuthal transect of the Breg River valley in areas near where it divides in two at a range of range of 725 meters involving more complex terrain slopes.
FIG. 11b shows the terrain elevation profile on a directional transect of the Breg River valley in areas near where it divides in two at a range of 725 meters involving more complex terrain slopes.
FIG. 12a shows the spaced elevation profiles derived from the DEM terrain elevations in the Breg River valley.
FIG. 12b shows the spaced elevation profiles derived from the polarimetric radar slope measurements in the Breg River valley.
FIG. 13 shows the scatter plots for the spaced elevation profiles derived from the polarimetric SAR tilts versus the DEM tilts derived from FIG. 12a and 12b.
FIG. 14a shows a typical signature obtained for P-band backscatter in a forested part of a study area on flat terrain.
FIG. 14b shows the effect of a positive slope on the shape of a polarimetric signature.
FIG. 15 shows the topography of the Fort Irwin study area from a Defense Mapping Agency 1:50,000 scale map with contours every 20 meters.
FIG. 16 shows an example of a typical Fort Irwin desert, open terrain, polarimetric signature at L-band.
FIG. 17a shows a comparison of the Fort Irwin elevation profiles derived in the azimuthal direction from polarimetric SAR and DEM data near the central portion of the mountain shown in FIG. 15.
FIGS. 17b shows a comparison of the Fort Irwin elevation profiles derived in the azimuthal direction from polarimetric SAR data and DEM data near the central portion of the mountains shown in FIG. 15.
FIG. 18 shows a scatter plot for the Fort Irwin azimuthal profiles comparing DEM-derived angles with angles derived from polarimetric SAR data.
DESCRIPTION OF THE PREFERRED EMBODIMENT
The polarimetric technique of measuring azimuth direction terrain slopes utilizes a polarimetric synthetic aperture radar (SAR) to provide a direct measure of terrain azimuthal slopes and a derived estimate of terrain elevation. Utilizing this measure of the azimuthal slopes and estimated terrain elevations, a one-dimensional terrain slope map over a wide area may be produced without any prior knowledge of the terrain. The terrain elevations are derived by integrating the slopes in the azimuthal direction and may be further refined so as to obtain absolute, rather than relative, elevation values by independently knowing at least one elevation "tie-point" along each slope profile being integrated. A complete two-dimensional topography elevation map can then be constructed from sets of elevation profiles spaced throughout the range direction.
This technique maximizes the electromagnetic scattering contact with the ground-plane for forested terrain slopes of much larger than a few degrees. Double bounce trunk-ground interactions are maximized for forested terrain by adaptively using polarizations which follow the position of the linear co-polarization (linear co-pol) maxima as the average terrain slope changes. Co-pol (that polarization having the same polarization a the transmit signal, HH and VV) signatures represent backscattered intensity plotted as a function of the polarization orientation angle, .PSI., and ellipticity, .chi.. (An ellipticity of 0.degree. corresponds to linear polarization, while an ellipticity of .+-.45.degree. corresponds to circular polarization. For an ellipticity of 0.degree., an orientation of 0.degree. corresponds to horizontal polarization and an orientation of 90.degree. corresponds to vertical polarization.) The co-pol signature is obtained by setting the receive polarization signal equal to the transmit polarization. This technique assumes that the dominant scattering mechanisms, which create a linear-polarization maximum in the polarimetric signature for flat terrain, will create a similar maximum for terrain with large slopes, but the location of this maxima will change in response to the larger slope. If the flat terrain maximum occurs, for example, at 0.degree. or 180.degree. (HH-polarization) then the maximum terrain slopes of 20.degree. will occur at approximately 20.degree. and -20.degree. at 160.degree.. The near equality of the terrain slope and the shift in the polarization maximum will occur over a wide range of incident angles .THETA..sub.i. This is because the two-bounce scattering in the vertical plane containing the trunk-ground approximation dihedral has a broad scattering pattern in the vertical plane. The forested terrain slopes measured by this method are not restricted to small angles. The preferred computational sequence is shown in Appendix I.
An expression for azimuthal terrain tilt .delta.=.delta.(S.sub.ij), where S.sub.ij are components of a scatter matrix is derived to predict the terrain slope, .delta., for a linear co-pol case. (The subscript ij means the polarization j is transmitted and polarization i is used to receive the scattered waves.) The equation is based on the concept that terrain tilts .delta. in the azimuthal direction and will shift the position of a new orientation maxima .PSI..sub.m to a new value .PSI..sub.m +.delta. when observed in a reference non-tilted plane. See, G. R. Valenzuela, Scattering of Electromagnetic Waves From a Tilted Slightly Rough Surface, Rad. Sci., Vol. 3, No. 11, pp. 1057-1066, 1968, which is hereby incorporated by reference in its entirety. For a vector E, the relationship between orthogonal coordinates [x,y] for the non-tilted surface and similar coordinates [x',y'] for a resolution cell tilted by an angle .delta. is given by ##EQU1##
A scattering matrix, [S.sub.ij ], of the form ##EQU2## is assumed, where a.sub.HH and b.sub.VV are orthogonal coordinates x',y' are parallel and perpendicular to the flat scattering plane whereas x,y are parallel to the tilted plane, respectively, and are constrained to be real. Scattering matrices of this form represent a valid scattering model for open terrain (slightly-rough scatter) and double-bounce (trunk/ground dihedral scatter) situations. To compute co-pol signatures in [x,y] coordinates, the scattering matrix is transformed into ##EQU3## where a and b are real. Equation (3) reduces to ##EQU4## Where S.sub.HH, S.sub.HV, S.sub.VV are the complex measured values of the scattering matrix [S.sub.ij ].sub.x,y from the tilted plane. The terrain tilt, .delta., is obtained by simultaneously solving the three relations for S.sub.HH, S.sub.VV, and S.sub.HV contained in Eq. (4). The solution for .delta. is ##EQU5##
The Stokes matrix [M.sub.ij ] and the polarimetric signature can subsequently be developed from the model for the scattering matrix [S.sub.ij ]. The Stokes matrix relates to the Stokes vectors for incident and scattered waves. The Stokes vector of a transmitting antenna is a real four-dimensional vector, whose elements are the four Stokes parameters describing the polarization of the transmitted wave. The scattering matrix describes how the scatterer transforms the illuminating electric field upon scattering, whereas the Stokes scattering operator describes how the scatter transforms the incident Stokes parameters upon scattering. See, Schuler et al., A Microwave Technique to Improve the Measurement of Directional Ocean Wave Spectra, Int. J. Remote Sensing, Vol. 16, No. 2, pp. 199-215, 1995; S. L. Durden et al., Modeling and Observation of the Radar Polarization Signature of Forested Areas, IEEE Trans. Geosc. and Remote Sensing, Vol. 27, No. 3, pp. 290-301, 1989; van Zyl et al., Imaging Radar Polarization Signatures: Theory and Observation, Rad. Sci., Vol. 22, No. 4, pp. 529-543, 1987; and Ioannidis et al., Optimum Antenna Polarizations for Target Discrimination in Clutter, IEEE Trans. Antenna Propa., Vol AP-27, No. 3, pp. 357-363, 1979; which are hereby incorporated by reference in their entirety.
The orientation, .DELTA..PSI., of the scattering maximum for the tilted terrain resolution cell observed in the non-tilted coordinate system has also been derived under the same constraints and .DELTA..PSI.=.delta.. Results using this expression produces profiles that follow the terrain tilts and are computationally fast. The constraint that all of the scattering terms must be real (i.e., in phase) was found to cause some error in the determination of .delta.. The measured slopes are less accurate and signal variance is greater than in a search-based algorithm.
A search-based formulation measures the location of the global maxima of a polarization signature, .sigma.(.chi.,.PSI.) in (.PSI.,.chi.) space for co-pol signature that differs from the above in that it does a direct search for signature maxima,and makes use of the full amplitude/phase information contained within the Stokes matrix, [M.sub.ij ]. (The polarization signature is simply a way to display the synthesized scattering cross section for different polarizations.) Expression for the terms, [M.sub.ij ], of the Stokes matrix in terms of [S.sub.ij ] are well known to those practicing in the art. This technique may also be used in searches for local co-polar maxima and cross-polarization (cross-pol) signatures. (Co-pol being the transmission of electromagnetic waves of one polarization and receiving the reflected electromagnetic wave in the same polarization, HH and VV. The cross-polarization signature is obtained by setting the ellipticity of the receive antenna to the negative of the transmit ellipticity, and the orientation of the receive antenna to that of the transmit antenna plus 90.degree.. Cross-pol on the other hand is the transmission of the electromagnetic waves in one polarization state and receiving the reflected electromagnetic wave in the opposite polarization state, HV.)
The location of the maxima is determined for each slant-range resolution cell (pixel). Changes in position of the maxima (.DELTA..PSI.) in the direction related to topography/dominant scatter mechanism, while changes (.DELTA..chi.) in the orthogonal direction are due to changes in ellipticity. Both shifts are stored as usable data products. The .PSI. changes are much larger than the changes in .chi., but this is not always the case. Stokes matrix, [M.sub.ij ], parameters are used for each pixel. These parameters are then averaged in both range and azimuth directions to reduce the statistical (speckle or fading noise) variation and a polarimetric signature is formed using the average values. The spatial dimensions used for each slope estimate, preferably, can be from 120 m.times.120 m for forested terrain and 30 m.times.30 m for open-terrain, however any convenient dimension may be chosen depending upon the users preference. The preferential spatial dimensions were chosen to keep the polarimetrically measured slope standard deviation/mean ratio approximately for each data set. Forest scatter at P-band thus requires more averaging than open-terrain at L-band for the same measurement accuracy. It should be noted, however, that smaller spatial averages still produce usable, albeit noisier, results.
The location of the global maxima of the co-pol signature is then computed and the deviation of the global maxima from the quiescent value used as the slope in the azimuthal direction. The technique is well suited for use in tilted semi-rough, or for forest terrain where the scatter is relatively homogenous and is dominated by some small number of scattering mechanisms. In areas of heterogeneous scatter the global peak becomes weaker, the unpolarized pedestal increases, and the slope measurement is less accurate. The latter case is to be encountered at the boundaries between forests and open terrain. This technique adapts automatically to either open or forested terrain conditions once the boundary is passed.
The polarization synthesis equation, an expression for .sigma.(.PSI.,.chi.) in terms of the Stokes matrix M.sub.ij and the transmit and receive polarization vectors, is then developed ##EQU6## where k is the radar wavenumber and T indicates a matrix response. Eq.(6) can be used to synthesize the scattering response for any (.chi.,.PSI.) polarization state.
The normalized cross-section is
.sigma.=s.sup.t M s (7)
where s is the Stokes transmitting (or receiving vector since they are equal for the co-pol case) and t denotes the vector transpose, and, without losing generality, the Stokes vector is ##EQU7## with the vector a satisfying a.sup.t a=1. Since the Stokes matrix, M.sub.ij, is symmetric, Eq. (7) can be
.sigma.=m.sub.11 +2b.sup.t a+a.sup.t Ca (9)
and b and C contain elements from the Stoke matrix, m, ##EQU8##
The optimization problem then becomes one of maximizing Eq. (9) subject to the constraint of a.sup.t a=1. The Lagrange multiplier method, supra, pp. 163-177, discussed in A. E. Bryson et al., Applied Optimal Control, Chapter 1, Blaisdell Publication Company, Waltham, Mass., Toronto, Ont., Canada, may be applied to produce an analytical solution. This method requires the solution of three, third-degree, simultaneous equations, which are difficult to solve analytically. Therefore, the preferred method of solution is the method of steepest descent, which is well known to those practicing the art.
Utilizing the method of steepest descent (or gradients), accelerates the computation for locating the maximum of the co-pol and uses iterative methods to locate the maximum or minimum. See, D. E. Kirk, Optimal Control Theory An Introduction, Prentice-Hall, Englewood Cliffs, N.J., pp. 331-342, 1970. The use of the Stokes matrix approach in finding the optimal polarization state to maximize the contrast between targets and clutter rather than other similar approaches is found to be more computationally efficient than other well-known methods.
The gradient of .sigma.(.chi.,.PSI.) with respect to a is,
.alpha..sigma./.alpha.a=2 (b+Ca). (11)
Starting from an initial value for a, the maximum is reached by iteratively updating on a unit sphere of a.sup.t a=1 in the direction of the gradien.
The maximum search procedure then requires:
(1) Setting the vector a to an initial value, namely, a.sup.t =[-1, 0, 0],
(2) computing the gradient using Eq. (11), and then
(3) updating the vector a by the equation
a'-a+.DELTA..alpha..sigma./.alpha.a (12)
where .DELTA. is the step size. The a' is then normalized by
a.sup.(new) =a'/(a').sup.t a'. (13)
(4) Then let a=a.sup.(new), and go back to step (2). The iteration terminates if a fixed number of iterations has been reached, or when
MAX (.vertline.a.sup.(new) (i)-a(i).vertline.)<0,0001 (14)
(5) Finally, compute the ellipticity and the orientation angles by
Ellipticity, .chi.=sin.sup.-1 (a.sub.3)/2,
Orientation, .PSI.=tan.sup.-1 (a.sub.2 /a.sub.1)/2. (15)
The figure .DELTA.=20/m.sub.11 works well. The division by reduces the variations of the gradient magnitudes that are larger for higher radar return areas. For returns from forested areas dominated by scattering from trunk-ground corner reflectors, co-pol signatures may have more than one local maximum. This situation differs from that occurring in open terrain (desert or grassy areas) where single-maximum slightly rough scattering is dominate. To obtain the second local maximum the above equation must be modified by initiating another value in a=[1,0,0], and then by following the same procedure. The .sigma. values for these two local maxima are computed using Eq. (9), and the vector a associated with the maximum .sigma. is used in the computation of .PSI. and .chi. as in Eq. (17), In general, forested terrain has two local maxima while open terrain only has one maximum. The foregoing procedure has the advantage that it automatically distinguishes open terrain from forested terrain.
Terrain slopes can be sensed for forested terrain at ground-level with an accuracy of 2.degree. (moderate relief areas) to 3.2.degree. and a correlation coefficient of greater than 0.8 when compared to digital-elevation map (DEM) values for a similar area. Terrain elevation profiles can be derived from the primary slope measurements and have accuracies of 8.4 m (moderate relief areas) to 18 m with correlation coefficients greater than 0.9. The technique described herein allows sensing of topography for forested terrain having slopes up to at least .+-.25.degree..
It is sufficient, for topographical studies, to use the maximum of the linear polarization case (.chi.=0) for the slope estimate. To find the maximum for the linear polarization case the calculation is simpler. The dimension of the vector a reduces to two; only a.sub.1 and a.sub.2 are to be searched for this optimization. The same procedure as the three dimension search case is applied, and this simplified calculation is about 40% faster than the one for locating both .PSI. and .chi..
Referring to FIG. 1, the polarimetric SAR data is utilized to compute the Stokes-Mueller matrix, [M]. The Stokes matrices for each pixel consist of a compressed 4.times.4 matrix whose terms are each products of complex terms of the scattering [S] matrix. When raw data is uncompressed (in a standard processing module) a matrix of range and azimuth pixels is obtained with each pixel having 10 numbers in it. These 10 numbers are the independent values of the 4.times.4 Stokes-Mueller matrix, M. The other 6 values of M can be derived using equations known to those practicing the art. The Stokes-Mueller Vector processor module, FIG. 2, inputs polarization orientation and ellipticity values (to any desired accuracy). The output is a quartet of numbers assembled as a 1.times.4 column vector, S, the Stokes Vector. The transpose is also constructed by making a 4.times.1 row vector, S.sup.t. These two quantities are used in the process module for forming Polarimetric Signatures .sigma.(.PSI.,.chi.).
The Polarimetric Signature module ingests complex polarimetric radar scatter [S] and Stokes-Mueller matrix [M] data obtained from the SAR remote sensing data-collection platform. The scatter matrix consists of four complex terms S.sub.VV, S.sub.HH (the vertical and horizontal polarization) and S.sub.VH (=S.sub.HV) the cross-pol terms. From [S] the components of the Stokes-Mueller matrix [M], a 4.times.4 matrix, can be computed using relations well-known to the practitioners of the art. The values of [M] are then used to compute the polarization signature .sigma.(.PSI.,.chi.) in the relationship
.sigma.(.PSI.,.chi.)=[S.sup.t ].multidot.[M][S]
where,
S.sup.t =[1, cos(2.chi.)cos(2.PSI.), cos(2.chi.)sin(2.PSI.), sin(2.chi.)]
S=column vector transpose of S.sup.t
.sigma.(.PSI.,.chi.)=The Polarization Signature
Referring to FIG. 3, input measured data consists of calibrated, independent estimates of the polarimetric Stokes-Mueller matrix, M, (ten numbers) for each image pixel (picture element). These 10 numbers are derived from the complex scattering matrix, S. The relations between S and M are well known to those practicing the art and are given by Eq. (1). The flow diagram of FIG. 3 shows (on the left) an array of image pixels in the radar range and azimuthal directions. Typically this array is 1024.times.1024 in size. The actual data is collected by polarimetric radar's mounted on an aircraft data-collection platform. Individual pixels are too noisy to yield good slope estimates. For this reason, Stokes-Mueller matrix values are first averaged for a number, N, of pixels in the range (vertical) direction. This averaging process is continued in the azimuthal (horizontal) direction for each of the one pixels. A strip 1-pixels long, centered at a range of N/2 pixels, is thus formed (strip #1). Subsequent overlapping strips of averaged Stokes-Mueller matrix values are formed by moving down by one range pixel and repeating the process to form overlapping strip #2. This process stops with a final strip #k being formed at the bottom of the image. The polarimetric signature is computed for each of the (average az pixels) in each of the k strips in the new (k.times.l) signature array. An efficient processor, called a Polarization Signature Maxima Location Module or Maximum Ascent processor, using the mathematical method of steepest descent, is then used to locate the position of the peak (or maximum) of the polarimetric signature in orientation, .PSI., or ellipticity, .chi.. Final processing is done in a Topographic Slope Map module which relates the changes in polarimetric orientation to terrain slope values for each of the k.times.l pixels. This module utilizes either (1) radar flat-earth incidence-angle Oi corrections or, (2) local pixel-by-pixel incidence angle data (if available). This final correction of the data adjusts the linear one-to-one relationship between orientation change and terrain slope in portions of the image where the incidence angle is small (.THETA.i<30) and corrections are needed to improve the slope estimate. Flat-earth .THETA.i corrections are known from the flight geometry. Local incidence angle corrections require a knowledge of terrain slopes in the range direction. This information is available if orthogonal direction data collection passes are made. Generally, the flat-earth correction will be enough to correct the slope map.
FIG. 4 shows the process needed to generate a polarimetric signature from the uncompressed, averaged Stokes-Mueller matrix data. These operations are performed on a pixel-by-pixel basis using the k.times.l matrix data created in FIG. 3. This M.sub.lk data is multiplied by a row-vector, S, which has been generated in a separate module. This output is then multiplied by the (column) transpose of S, S.sup.T. The result is an k.times.l size matrix of .sigma..sub.k,l .PSI.,.chi. values. Each of the .sigma..sub.k,l matrixes is itself 180.times.90 values which are the value of the signature for all possible orientations (180 values) and ellipticities (90 values) measured to an accuracy of +0.5.
The matrix of polarization signatures are then inputted to a following module, the Polarization Signature Maxima Location Module or Maximum Ascent Processor module, FIG. 5, locates the polarization maxima (in (.PSI.,.chi.) space) on a pixel-by-pixel basis. There is often more than one maxima. The operations of this module, implemented using a microprocessor, implement the mathematical Method of Steepest Ascent (or Descent) which is an efficient means for locating maxima and minima. In this application there is a real possibility of the existence of more than one maxima. For this reason the processing flow breaks into two parallel paths involving two initial values, initial Stokes vectors of a=a'=[-1,0,0] and a'=[1,0,0] are used. The paths are identical except for the point at which the search for the maxima begins. The first path (left in figure) starts with the value a=a'=[-1.0.0]. This point corresponds to a point in [.PSI.,.chi.] space of [90.degree.,0.degree.]. The second path (right in figure) starts with the second value a'=[1,0,0] which corresponds to a point in [.PSI.,.chi.] space of [0.degree.,0.degree.]. The rationale for choosing these two starting points was that (1) all single bounce terrain scatter produces peaks with .chi.=0.degree. and .PSI. angle spacings of 90.degree., or 180.degree., and (2) double-bounce scatter produces values with .chi..noteq.0.degree., but with the mean ellipticity value of the scatter .chi.=0 and, again, the peaks occur at .PSI. spacings of 90.degree., or 180.degree.. Terrain slopes will, of course, move the peaks away from these flat-earth locations, but the two chosen initial values are efficient start points for locating all the peaks. The search for the polarization peaks is done in [.PSI.,.chi.] space using a three-component vector a which is the part of the Stokes-Mueller vector S which actually varies as a function of .PSI. and .chi.. The process of finding the maxima .sigma..sub.1 (or 2) (.chi.,.PSI.) is an iterative walking process up .sigma. hills in which successive "steps" are always made in the direction of the steepest gradient. This walking process is subject to the one-constraint that a.sup.T a=1. This condition means that each normalized back into a sphere a.sup.T a=1=a.sub.1.sup.2 +a.sub.2.sup.2 +a.sub.3.sup.2. This condition is demanded by a realizability condition on co-polar scattering solutions. After normalization the old value a compared with the new value. If max(1 a.sup.(new) -a.sub.i 1)<0.0001 then the maximum has been found and the looping stops. If the difference is too great it continues. The processor iterates solutions and step sized until the paths reach maxima .sigma..sub.1 and .sigma..sub.2 then .sigma..sub.1 (.PSI.,.chi.) is the maxima. Otherwise, .sigma.0.sub.2 (.PSI.,.chi.) is the largest maxima. Once a satisfactory maxima has been found .chi., and .PSI. values are computed by .chi.=Sin.sup.-1 (a.sub.3)/2 and .PSI.=tan.sup.-1 (a.sub.2 /a.sub.1)/2. Finally, if maxima are found for the two looping paths which have different (.chi.,.PSI.) solutions, then the larger one is chosen. In other words, the polarization signatures for each image pixel are ingested by the Polarization Signature Maxima Location Module to determine the (.PSI.,.chi.) space location of the largest signature maxima. The signature maxima, whose shift from a flat-earth location may be related to slope, are then averaged to improve their signal-to-noise ratio. The processing of the Orientation Averaging Module of the Topographic Slope Map Module combines a number (typically 50-100 pixels) of the individual pixel maximum locations together to obtain an accurate estimate. This averaging procedure reduces the effects of speckle and noise so that a more accurate estimate of the changes in orientation .delta..PSI. is obtained. At this point in the flow either terrain slope or elevation matrices can be formed and displayed. The formation of terrain elevation maps requires two additional processing steps. First, the elevations for each row of azimuthal pixels must be initialized by a known elevation "tie-point". Secondly, the slope values must be integrated in the azimuthal direction. Once these two steps are completed a terrain elevation map may be produced by carrying out the initialization and integration for each row in the range direction.
The integrated slope elevation matrix, FIG. 6, is required when topographic elevation maps are the final product rather that slope maps. The k.times.l values which are outputted by the Topographic Slope Map module are fed to a boxcar integrator which integrates the slope data into elevation data. The initial elevations at the start of the integration must be known (one per azimuthal strip) from external sources. The elevation data is stored as a k.times.l output matrix in the processor.
The output terrain elevation map may be displayed as a surface plot versus range and azimuth distances in meters. If the original radar image can be registered with several known locations on the ground, then this surface can be plotted versus latitude and longitude as well.
In the apparatus for implementing the foregoing method, referring to FIG. 7, a polarimetric synthetic aperture radar (SAR) 22, operating, for instance, at the L-band frequency of 25 cm, alternately transmits horizontally and vertically polarized pulses. During the interpulse period, both polarizations are received and amplitude and phase measurements are passed through an analog-to-digital converter 24 where the radar's analog signal is converted into a digital data bit stream and formatter 26 where the digital bit stream is formatted and then recorded and stored directly in a data storage device 28, such as a high density magnetic digital tape recorder or equivalent laser disk recording device. See, J. J. van Zyl, Unsupervised Classification of Scattering Behavior Using Radar Polarimetry Data, IEEE Trans. Geosc. and Remote Sensing, Vol. 27, No. 1, pp. 36-45, which is incorporated herein in its entirety, for a discussion of the data acquisition techniques. The data is collected in or converted to a digital domain for image manipulation purposes and stored in the data storage device 28. The digitally formatted stored polarimetric SAR electromagnetic reflections are direct measures of the complete scattering matrices for each resolution element. At the end of the data acquisition phase, the data tape or laser disk containing the digitally formatted scattering matrices is removed from the storage device 28 and interfaced with a playback unit 32 and digital correlator 32.
This technique is about 20 times faster than currently utilized methods and speeds up the overall computation of terrain elevations by a factor of five. The method of steepest descent has an error of smaller than 0.01.degree., more accurate than current methods.
In an experimental evaluation of the above-stated topographical mapping techniques, the Naval Research Laboratory obtained a 1989 data-set of NASA/JPL polarimetric AIRSAR flown on a DC-8 aircraft over a region near Villingen/Schwenningen, Germany in the Black Forest region. This area has been overflown in both the MAESTRO-1 1989 and MAC-Europe 1991 campaigns to provide wide-coverage polarimetric SAR images which could be compared with forest classification studies done on the ground. Because of these studies considerable information on local topography and forest-type was available. The test set forth below utilized the JPL/AIRSAR polarimetric SAR data acquired during MAESTRO-1 1989 and was greatly expedited by using a co-registered (1) calibrated P-band SAR image, and (2) a georeference file for the same area. The georeference file contained values of seven terrain/radar geometric variables, including terrain elevation and local incidence angle, which were re-binned to match the SAR image pixels. The DEM contained within the georeference file was made by the State of Baden-Wurttemberg using a stereo photography technique. This DEM is, therefore, a measure of the terrain canopy, rather than ground, level. The topography was measured on a 30.times.30 m grid by the Baden-Wurttemburg government study. The rms elevation error of the DEM over the portions of the study area without extreme slopes is .+-.3 m. Derivatives of elevations from this DEM were used as estimates of local terrain slopes.
The AIRSAR data was acquired during a pass from west to east over the Black Forest study area. The image contained 1024 pixels (range direction) by 752 pixels (azimuth direction) each pixel having dimensions in the slant range 6.6 m by 12.1 m (4-look data), respectively.
The topography of the area of the Black Forest consisted, in essence, of a forested gently rising (3.degree.-4.degree. slope) plateau bounded on either side by deeply indented river valleys formed by the Breg and Brigach Rivers. This area was a useful study area because most of the topographic changes occurred in the azimuthal direction--and thus the complications due to radar height-related "lay-over" in the range-direction were largely avoided. Forest terrain slopes leading down to the Breg River often reached values of 25.degree.-30.degree.. The topography of the indented is shown in FIG. 8 with the contours represented in meters above a reference level. The georeference file terrain elevation values (the DEM) were collected on a 30.times.30 m grid.
All estimates of terrain slope reported here by either the radar, or georeference file, were made with 121 m (10 pixel) averaging in the azimuthal direction and 119 m (19 pixel) averaging in the range direction. The convention was taken that East-West terrain slopes that are upward above the horizontal are considered positive.
Profiles transecting the Breg River valley were measured at different North-South locations. FIG. 9a gives an example of a terrain slope profile obtained by a transect of the Breg River valley above a datum of 300 m. In FIG. 9a, and the subsequent figures, values obtained from the DEM are shown as dashed lines and the terrain slopes obtained from the polarimetric SAR are shown by a solid line. FIG. 9a traces the plunge from the high ridge of the forested plateau past an upward spike (German highway 1-180) to the Breg River (where the slope=0) and up the opposite side of the valley. An estimate of the terrain elevation profile is given in FIG. 9b above a datum of 300 m. FIG. 9b was obtained by integrating the radar slope data. The value of elevation at zero (azimuthal) distance was initialized to be equal to the DEM values. FIGS. 10a shows the terrain azimuthal slope profile comparison between those shown on the digital-elevation map (DEM) and those obtained by the polarimetric synthetic aperture radar (SAR) on a azimuthal transect of the Breg River valley at a range above a datum 725 m involving more complex terrain slopes. FIG. 11b shows the terrain elevation profile on a directional transect of the Breg River valley at a range of 725 meters. FIG. 11b transects the Breg River valley in areas near where it divides in two (FIGS. 11a and b) yielded more complex slope profiles but again the correlation between DEM and measurements by the polarimetric SAR spaced across the Black Forest study area and the Breg River gave results similar to those of FIGS. 90a and b and 10a and b. FIGS. 12a and b gives spaced elevation profiles derived from the polarimetric radar slope measurements and taken directly from the DEM. FIGS. 12a and b show good elevation agreement and feature correlation but some under-estimation of the depth of the valley is evident. FIG. 13 gives scatter plots for these same elevation profiles for the Black Forest study area comparing derived DEM slopes with polarimetric SAR derived slopes for all profiles. In FIG. 13 the dashed line at 45.degree. represents perfect agreement between the measurement of the DEM and polarimetric SAR derived slopes.
Slope profiles derived from the lower frequency L-band data correlated reasonably well with the P-band profiles. The larger slope-estimation variance at L-band, and at a C-band experiment, indicates that canopy, and/or branch scattering is dominant for these datasets.
The accuracy (rms error) and correlation coefficient (SAR/DEM) for the technique is given in Table 1. The rms errors/correlations achieved are judged relative to the DEM. The DEM itself only had a .+-.3 m elevation accuracy for the relatively flat areas in the image and overall a 6 m quantizing error.
The P-band signatures obtained throughout the Black Forest study area on both level and tilted terrain are characteristic of double-bounce scatters. These signatures show the aggregate effect at P-band of tree trunk-ground interactions, branch scattering, and direct-ground contributions. FIG. 14a shows a typical signature obtained for P-band backscatter in the forested part of a study area on flat terrain. The signature for flat terrain is characterized by major peaks at orientations, .PSI., of 0.degree. and 180.degree. (horizontal polarization), and a smaller peak at .PSI.=90.degree. (vertical polarization). The flat-terrain signature is symmetric to either side of the orientation .PSI.=90.degree.. FIG. 14b shows the effect of a positive slope (height increasing from left to right in the azimuthal direction) on the shape of the polarimetric signature. The major effect of a known azimuthal slope of 22.5 is to move the position of the peak at 180 to 157 on the .chi.=0 axis. This shift in the position of the polarization peak is proportional to the terrain slope in the azimuthal direction.
Polarimetric SAR measurements of terrain slopes in the Black Forest study up to .+-.25.degree. have been measured and confirmed by comparison with the DEM. Operation at P-band, or at longer wavelength, offers a chance (depending on the biomass density and type for penetration through the forest canopy to map the underlying topography. For forests similar to the study area in the Black Forest penetration is likely for polarizations near the signature maxima.
This test confirmed that terrain slopes can be sensed for forested terrain at ground-level with an accuracy of 2.degree. (moderate relief areas) to 3,2.degree. at the Breg River valley and a correlation coefficient of greater than 0.80 when compared with DEM values. Terrain elevation profiles were derived from the primary slope measurements and have accuracies of 8.4 m (moderate relief areas) to 18 m in the Breg River valley with correlation coefficients of greater than 0.92. The technique allows sensing of topography for forested terrain having slopes up to at least .+-.25.degree.. The measurement of topography at ground-level rather than forest canopy level has not been shown by any other remote sensing technique known today.
A second polarimetric SAR dataset was analyzed where the scattering is from mountainous desert terrain on the National Training Center near Ft. Irwin in southeastern California to establish that the polarimetric SAR technique would work when the terrain is open rather than forested. Because fully-polarimetric SAR imaging systems have, generally, been developed at L-band or higher frequencies, a second objective was to show that usable results are obtainable for open-terrain at L-band frequencies.
The data utilized was NASA JPL/AIRSAR data. Images produced from the dataset show a portion of the Tiefort mountain range, Drinkwater Lake, and the surrounding Mojave desert basins. In general the mountains in the image are rugged and devoid of trees and other large vegetation. Topographic slopes of up to .+-.50.degree. and elevation differences of 487 m exist in the imaged area. FIG. 15 shows the topography of the Fort Irwin study area from a Defense Mapping Agency 1:50,000 scale map with contours every 20 meters. The valleys contain low desert vegetation types--but again, no forested areas.
This study area was selected because of the existence of a very accurate DEM covering an area of 5.6 km.times.7 km. This DEM is constructed on a 5 m post (pixel) spacing with an accuracy of 0.3 m. FIG. 16 is an example of a typical Fort Irwin desert, open terrain, polarimetric signature at L-band. Note that the signature maxima occurs now at about .PSI.=90.degree. (VV-pol). Application of the foregoing computational technique to the Fort Irwin study area yielded slope/elevation profiles which correlated well with known mountain and desert basin features.
From the dataset, a rectification, or data co-registration, method suggested by Leberl (F. W. Leberl, Radargrammetric Image Processing, Artech House, Chapter 8, 1989) was applied instead which uses terrain features within the SAR image and the DEM. The SAR/DEM databases were rectified using localized mountain and desert basin sub-areas of the image. Multiple terrain features with approximately the same elevation were employed as tie-points. Terrain slope and elevation azimuthal profiles were then developed for these sub-areas. Two examples of elevation profiles derived near the central portion of the mountain are given in FIGS. 17a and b show a comparison of the Fort Irwin elevation profiles derived in the azimuthal direction from polarimetric SAR and DEM data near the central portion of the mountain shown in FIG. 16.
FIG. 18 shows a scatter plot for the Fort Irwin azimuthal profiles comparing DEM-derived angles with angles derived from polarimetric SAR data. In FIG. 18 the solid line indicates perfect agreement between the two elevation measurements. The azimuthal profiles in FIG. 18 consist of 44 profile having 50 m separation and are taken from the central 2 km (range) by 5 km (azimuth) portion of the mountain. The rms errors determined by comparing SAR and DEM measurements for these azimuthal profiles are also given in Table 1. The Fort Irwin study was made more difficult because of radar layover, shadowing and other effects in the rugged, mountainous terrain. The Fort Irwin rms errors shown in Table 1 are an initial estimate using a feature-based rectification technique.
Using the techniques described herein, polarimetric SAR systems using aircraft, space shuttle or satellite platforms are capable of providing topographic information over wide areas. The synthetic aperture radar is well known to those skilled in the art and preferably comprises an P-band (with a wavelength of approximately 68 cm), L-band (approximately 21 cm) or C-band (approximately 5.65 cm) having quad polarization or any combination of HH, VV, HV, VH, RC, LC polarizations and which is capable of penetrating vegetation, particularly tree foliage. This same SAR data is also useful in the accurate extraction of geophysical parameters (soil moisture, biomass density, crop type, etc.) when the underlying topography must be known and taken into account. Polarimetric SAR implemented at P-band, or lower frequencies, can be used as a measurement tool which can aid in solving the phase ambiguity problems found in interferometric SAR (IFSAR). Polarimetric SAR slope and elevation measurements can provide bounds on the IFSAR phase path.
Operation a P-band, or at longer wavelengths offers a chance (depending on the biomass density and type) for penetration through the forest canopy to map the underlying topography. (However, at C-band frequencies, the electromagnetic waves will not penetrate significantly into the forest, and the resulting scattering will be primarily from the branches and the needles.) The method for processing the polarimetric radar information adeptly handles transitions between spatial areas dominated by disparate scattering mechanisms--such as those occurring between forest areas and open fields.
Geophysical parameter extraction studies utilizing polarimetric SAR data are affected by local topography. The topographic measurement technique described herein provides co-registered estimates of local slopes which are used to improve the accuracy of such studies. A complete wide-area two-dimensional topographic slope and elevation map may be produced of open-terrain topography during day/night under all weather conditions.
The concepts of this invention, although preferably addressed to the polarimetric synthetic aperture radar (SAR) and usable with interferometric SAR, may also utilize polarimetric real aperture radar (RAR) systems. The only limitation placed on the use of RAR would be the size of the antenna required and its integration into an airborne carrier. In utilizing interferometric SAR the ability to achieve adequate spacing between antennas would be the most inhibiting limitation.
It will be understood by those skilled in the art that still other variations and modifications are possible and can be affected without detracting from the scope of the invention as defined by the claims. ##SPC1##
Summary of Technique Performance
High        All Terrain
High  Terrain
Study  RMS Error
RMS Error
Coefficien
2.0.degree.
8.4 m   18 m
5.6 m 23.5 m
1. A polarimetric processor for measuring azimuth direction terrain slopes comprised of:
a radar for transmitting and receiving analog electromagnetic signals of alternately horizontally and vertically polarization;
an analog-to-digital converter where the analog electromagnetic signals are converted into a digital data bit stream;
a formatter for formatting the digital bit stream;
means for recording and storing the digital data bit stream;
a playback unit for removing the digital data from the storage means;
a digital correlator for correlating the digital data bit stream;
a computer for receiving the correlated digital data bit stream and computing
(a) a Stokes-Mueller matrix, M, utilizing the digitized analog electromagnetic signals of alternately horizontally and vertically polarization extracted from the playback unit and correlated;
(b) a polarimetric signature,.sigma. (.PSI..chi.), utilizing the Stokes-Mueller matrix, M;
(b) a first, a=a'=[-1,0,0], and second initial value, a'=[1,0,0], for a pixel or pixels;
(c) a first gradient utilizing the method of steepest descent for the first and second initial values;
(d) updating the first and second initial values utilizing the gradient;
(e) normalizing the first and second initial values;
(f) repeat steps (c)-(e) utilizing the normalized first and second values until the maximum has been found;
(g).sigma..sub.1 and.sigma..sub.2 utilizing a new first and second values;
(h) a comparison of.sigma..sub.1 and.sigma..sub.2,
(i) a value for Ellipticity,.chi.=sin.sup.-1 (a.sub.3)/2, and Orientation,.PSI.=tan.sup.-1 (a.sub.2 /a.sub.1)/2;
(j) a combination of individual pixel maximum locations;
(k) a initialization of elevations for each row of azimuthal pixels by a known elevation point;
(l) an integration of slope values in an azimuthal direction; and
means for plotting the ellipticity and orientation to produce a presentation that is a direct measure of terrain azimuthal slopes and a derived estimate of terrain elevation.
2. A polarimetric processor, as in claim 1, wherein said radar is polarimetric synthetic aperture radar system.
3. A polarimetric processor, as in claim 1, wherein said radar is interferometric synthetic aperture radar system.
4. A polarimetric processor, as in claim 1, wherein said radar is polarimetric real aperture radar system.
5. A method for measuring azimuth direction terrain slopes comprised of:
transmitting and receiving analog electromagnetic signals of alternately horizontally and vertically polarization;
converting the analog electromagnetic signals into a digital data bit stream;
formatting the digital bit stream;
recording and storing the digital data bit stream;
removing the digital data from storage;
correlating the digital data bit stream;
plotting the ellipticity and orientation to produce a presentation that is a direct measure of terrain azimuthal slopes and a derived estimate of terrain elevation.
4551724 November 5, 1985 Goldstein et al.
4922254 May 1, 1990 Schuessler et al.
4975704 December 4, 1990 Gabriel et al.
5053778 October 1, 1991 Imhoff
5142291 August 25, 1992 Chang et al.
5313210 May 17, 1994 Gail
Madsen et al., "Analysis and Evaluation of the NASA/JPL TOPSAR Across-Track nterferometric SAR System", IEEE Trans. Geosc. and Remote Sensing, vol. 33, No. 4, pp. 383-391, Mar. 1995. Rodriguez et al., "Theory and Design of Interferometric Synthetic Aperture Radars", IEEE Proceedings-F, vol. 139, No. 2, pp. 147-159, Apr., 1992. Li et al., "Studies of Multibaseline Spaceborne Interferometric Synthetic Aperture Radars", IEEE Trans. Geosc. and Remote Sensing, vol. 28, No. 1, pp. 88-97, Jan., 1990. Valenzuela, "Scattering of Electromagnetic Waves From a Tilted Slightly Rough Surface", Radio Science, vol. 3, No. 11, pp. 1057-1066, Nov., 1968. Schuler, et al., "A Microwave Technique to Improve the Measurement of Directional Ocean Wave Spectra", Int. J. Remote Sensing, vol.16, No. 2, pp. 199-215, 1995. Durden et al., "Modeling and Observation of the Radar Polarization Signature of Forested Areas",IEEE Trans. Geosc. and Remote Sensing, vol. 27, No. 3, pp. 290-301, May 1989. van Zyl et al., "Imaging radar polarization signatures: Theory and Observation", Radio Science, vol. 22, No. 4, pp. 529-543, Jul.-Aug. 1987. Ioannadis et al., "Optimum Antenna Polarizations for Target Discrimination in Clutter",IEEE Trans. Antennas and Propagation, vol. AP-27, No. 3, pp. 357-363, May 1979. A. E. Bryjon et al., Applied Optimal Control, Ch. 1, Blasdell Publication Company, Waltham, MA, Toronto, Ont. Canada. Kirk, "Optimal Control Theory an Introduction", Prentice-Hall, Englewood Cliffs, NJ, pp. 331-342, 1970. van Zyl, "Unsupervised Classification of Scattering Behavior Using Radar Polarimetry Data", IEEE Trans. Geosc. and Remote Sensing, vol. 27, No. 1, pp.36-45, Jan. 1989. Schuler, et al., "Polarimetric SAR Image Signatures of the Ocean and Gulf Stream Features", IEEE Trans. on Geosc. and Remote Sensing, vol. 31, No. 6, pp. 1210-1221, Nov. 1993. van Zyl, "The Effect of Topography on Radar Scattering from Vegetated Areas", IEEE Trans. on Geosc. and Remote Sensing, vol. 31, No. 1, pp. 153-160, Jan 1993. Doug et al., "Studies of the Cylinder-Ground Double Bounce Scattering Mechanism in Forest Backscatter Models", IEEE Trans. on Geosc. and Remote Sensing, vol. 33, No. 1, pp. 229-231, Jan 1995. Madsen et al., "Topographic Mapping Using Radar Interferometry: Processing Techniques", IEEE Trans. on Geosc. and Remote Sensing, vol. 31, No. 1, pp. 246-255, Jan. 1993. Goldstein et al., "Satellite Radar Interferometry: Two-dimensional Phase Unwrapping", Radio Science, vol. 23, No. 4, pp. 713-720, Jul.-Aug. 1988. Schuler et al., "Measurement of Topographic Surface Slopes using Polarimetric SAR Images", Int. Geosc. and Remote Sensing Symp., Cal. Inst. of Tech., Aug. 8-12, 1994. Schuler et al., "Measurement of Topographic Surface Slopes using Polarimetric SAR Images", Poster Presentation on display at Int. Geosc. and Remote Sensing Symp., Cal. Inst. of Tech., Aug. 8-12, 1994. Arfken, "Mathematical Methods for Physicists", Academic Press, New York, N.Y., Sec. 7.4, pp. 428-436, 1985. Swartz et al., "Optimal Polarizations for Achieving Maximum Contrast in Radar Images", J. Geophy. Res., vol. 93, No. B12, pp. 15, 252-15,260, Dec. 10, 1988.
Filed: Oct 10, 1995
Date of Patent: Sep 3, 1996
Assignee: The United States of America as represented by the Secretary of the Navy (Washington, DC)
Inventors: Dale L. Schuler (Fairfax Station, VA), Jong-Sen Lee (Great Falls, VA)
Primary Examiner: John B. Sotomayor
Attorneys: Thomas E. McDonnell, Charles J. Stockstill
Current U.S. Class: 342/25; With Polarization (342/188); Mapping (342/191)
International Classification: G01S 1390;


text:
Return to Speaker page Get a Free Ticket Tweet about it
Kiera Carter
How editorial drives customer engagement and brand awareness
Kiera Carter, editorial director of Wix's blog network, will help you engage both existing and potential customers with content that educates, inspires, and resonates. She'll discuss the lifecycle of an editorial piece, from conception to promotion, for max impact across platforms.
About Kiera Carter
Kiera Carter is a magazine editor turned content marketer who has managed editorial at high-traffic fitness, food, beauty, wellness, and business sites. She is now the editorial director of Wix, where she oversees blogs for professionals across industries.
In a past life, she was the executive digital editor of Shape magazine, where she oversaw the day-to-day editorial operations and creative of the website, including SEO-driven features, news, videos, emails, and large-scale campaigns that reached millions of readers. She has also held staff positions at Men's Health and Prevention, and her work has been nominated for a National Magazine Award, the most prestigious in the industry. This means Kiera knows what people search for and share, plus what inspires them, makes their lives better, and resonates long-term. Think: content strategy with a soul.


text:
by Kate M. Kelly March 12, 2018
posted in Public Policy
The Color of Law: A Forgotten History of How Government Segregated America
Richard Rothstein, author of The Color of Law
The Color of Law Documents State-Sponsored Residential Segregation
On Wednesday, May 16, 2018, Monarch Housing Associates in partnership with Seton Hall University Law School, the Anti-Poverty Network of NJ, and NJ Institute for Social Justice will host a Public Policy Forum on The Color of Law.
Keynote speaker and The Color of Law author Richard Rothstein will present the national research in his book and take questions from the audience. Rothstein is a research associate of the Economic Policy Institute and a Fellow at the Thurgood Marshall Institute of the NAACP Legal Defense Fund.
The Color of Law expands upon and provides a national perspective on Rothstein's recent work that has documented the history of state-sponsored residential segregation, as in his report, The Making of Ferguson.
In the book, Rothstein writes, "We have created a caste system in this country, with African-Americans kept exploited and geographically separate by racially explicit government policies," he writes. "Although most of these policies are now off the books, they have never been remedied and their effects endure."
A June 20, 2017 New York Times review of The Color Law calls the book "A Powerful, Disturbing History of Residential Segregation in America."
"One of the great strengths of Rothstein's account is the sheer weight of evidence he marshals. A research associate at the Economic Policy Institute, he quite simply demolishes the notion that government played a minor role in creating the racial ghettos that plague our suburbs and inner cities."
Rothestein is also the author of:
Grading Education: Getting Accountability Right (2008) and
Class and Schools: Using Social, Economic and Educational Reform to Close the Black-White Achievement Gap (2004).
The Way We Were? Myths and Realities of America's Student Achievement (1998).
The Charter School Dust-Up: Examining the Evidence on Enrollment and Achievement (co-authored in 2005); and
All Else Equal: Are Public and Private Schools Different? (co-authored in 2003).
Writes the NYT, "In his preface, Rothstein writes that America has a constitutional obligation to remedy de jure segregation in housing, and that its story must be told. While the road forward is far from clear, there is no better history of this troubled journey than "The Color of Law."
National Public Radio (NPR) named The Color of Law as one of its 2017 Great Reads.
Speaking with Terry Gross "The segregation of our metropolitan areas today leads … to stagnant inequality, because families are much less able to be upwardly mobile when they're living in segregated neighborhoods where opportunity is absent," Rothstein says. "If we want greater equality in this society, if we want a lowering of the hostility between police and young African-American men, we need to take steps to desegregate."
Also in May 2017, Ta-Nehisi Coates, national correspondent for The Atlantic interviewed Rothstein.
Housing segregation is not unique to the South and Rothestein's research is very relevant to New Jersey. A May 5, 2017 Slate review of The Color of Law writes,
"Rothstein persuasively debunks many contemporary myths about racial discrimination. He goes after, for instance, the resilient misconception that racial separation was only government policy in the Jim Crow South, and that black entrants into neighborhoods cause white homeowners' property values to fall. In one powerful section on zoning policies, Rothstein traces how hazardous waste sites were concentrated in segregated black neighborhoods. The episode mirrors the displacement of black families by urban renewal and interstate highway construction in mid-20th century."
The Color of Law is available online from Amazon, Barnes and Noble, along with other booksellers.
Follow the event on Twitter.
#ColorofLawNJ Tweets
Summary of the Color of Law
NY Times Review
Fresh Air Review
Slate NY Review
Follow us on Apple News
Subscribe to Our Newsletter for News You Can Use Everyday
Subscribe to Our Weekly Newsletter Delivered on Friday
Home » Posts » The Color of Law: A Forgotten History of How Government Segregated America
Previous Post: Governor Murphy Delivers First Budget March 13
Next Post: Investing in New Jersey's Future Will Require New Budget Revenues
Read: October 2017
The Color of Law by Richard Rothstein
by Richard Rothstein
The Color of Law by Richard Rothstein Identifies Local, State and Federal Policies Responsible for America's Segregated Cities
In 2017, Richard Rothstein's The Color of Law: A Forgotten History of How Our Government Segregated America was one of ten finalists on the National Book Awards' long list for the best nonfiction book of 2017.
The National Low Income Housing Coalition (NLIHC) has announced that Rothstein will be a speaker at its 2018 Housing Policy Forum.
The Economic Policy Institute writes that "In The Color of Law (published by Liveright in May 2017), Richard Rothstein argues with exacting precision and fascinating insight how segregation in America-the incessant kind that continues to dog our major cities and has contributed to so much recent social strife-is the byproduct of explicit government policies at the local, state, and federal levels."
Rothstein is a former columnist for the New York Times, a research associate at the Economic Policy Institute, and a Fellow at the Thurgood Marshall Institute of the NAACP Legal Defense Fund.
Writes the Economic Policy Institute, "Rothstein has spent years documenting the evidence that government not merely ignored discriminatory practices in the residential sphere, but promoted them."
Its review continues with "The impact has been devastating for generations of African-Americans who were denied the right to live where they wanted to live, and raise and school their children where they thought best."
In May 2017, Rothstein was interviewed by Terry Gross on NPR's Fresh Air. "Rothstein's new book, The Color of Law, examines the local, state and federal housing policies that mandated segregation. He notes that the Federal Housing Administration, which was established in 1934, furthered the segregation efforts by refusing to insure mortgages in and near African-American neighborhoods – a policy known as 'redlining.' At the same time, the FHA was subsidizing builders who were mass-producing entire subdivisions for whites – with the requirement that none of the homes be sold to African-Americans."
Economic Policy Institute Review
Terry Gross' interview with Richard Rothstein
Ta-Nehisi Coates interview with Richard Rothstein


Brie has been with us for almost a year and we still think of her as new, yet she conducts her business as if she has been doing this for a long time. With over seven years of experience in real estate transactions, having worked as a legal assistant for several Williamstown attorneys, Brie has an added advantage in her skills as a Realtor. Already working closely with several buyers and sellers, she is proving to be someone with good instincts and know how.
As with all of our agents, Brie has completed the Brian Buffini Peak Producer's course, a twelve week training program that gives agents the strategies to build a rock-solid real estate business. Brie is making good use of all of the tools she has learned and it shows in the activity she is experiencing. We at Maple Leaf Realty are thrilled to have Brie working with us and are expecting great things from her this year.
Brie is married with two young daughters and when not working on her new career, enjoys every moment she can with her family and the occasional night out with her husband.
Experienced or not, all of our new agents have a mentor in each and every one of us at Maple Leaf Realty so that our customers and clients have the full support, knowledge and experience of the entire company. Please give Brie a call (802-441-4739), or email Brie@BrieBurdge.com to assist you with buying or selling your home. You'll be glad you did.