<p>The term 'off-Rowland-circle <strong>telescope</strong>' is a bit awkward, I think normally we would call the arrangement of FORTIS an off-Rowland-circle spectrograph, and they probably just used the word 'telescope' to make their acronym sound better. If we're being pedantic, then I think everything before the primary focus would be the telescope, and everything after is the spectrograph.</p>
<p>There are certainly on-Rowland-circle spectrographs, it's the simplest type of reflective spectrograph, and the <a href="https://arxiv.org/abs/astro-ph/0407464" rel="nofollow noreferrer">FORTIS paper</a> linked above by @Keith McClary mentioned several: HUT, OREFUS and FUSE.</p>
<p>In terms of an off-Rowland-circle spectrograph, I think the footnote you mentioned on page 4 says it all:</p>
<blockquote>
<p>In a Rowland circle spectrograph all the rays at wavelengths satisfying the grating equation entering a slit placed on a circle, with
diameter is equal to the radius of the concave grating, are diffracted to a tangential focus on the same circle.</p>
</blockquote>
<p>This is in contrast to FORTIS, which has magnification. In the figure below, I've taken the optical layout from the
<a href="https://arxiv.org/abs/astro-ph/0407464" rel="nofollow noreferrer">FORTIS paper</a> and annotated it with an approximate Rowland circle in a bold black line. From this figure, we can see that the primary focus is inside the Rowland circle, and the secondary focus (at the detector) is outside the Rowland circle. For FORTIS to be a on-Rowland-circle spectrograph, both the primary and secondary focus need to be the same distance from the grating and on the Rowland circle.</p>
<p><a href="https://i.sstatic.net/a1uxt.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/a1uxt.png" alt="FORTIS optical layout with annotated Rowland circle" /></a></p>

CC BY-SA 4.0
2022-09-13T11:33:58.303Z
Thanks! Can you also address "What is an 'Off Rowland-circle ***Telescope***'"? Is it a  Rowland-circle spectrometer duct-taped to a telescope, or is there some telescopic nature to the Rowland-circle optical design, or something else entirely?
uhoh
CC BY-SA 4.0
2022-09-13T12:25:14.693Z
In my opinion, an off-Rowland-circle telescope is a bit of an awkward term that they probably used to make their acronym sound better. I haven't heard that term before, but I just took it to mean your former suggestion, a spectrometer duct taped to a telescope.
Roy Smart
CC BY-SA 4.0
2022-09-13T12:35:44.363Z
@RoySmart That is correct :P And yes they have to make their acronyms sound nice! :D
DialFrost
CC BY-SA 4.0
2022-09-13T05:29:07.690Z
2022-09-13T18:56:59.717Z
2022-09-13T18:56:59.717Z
Roy Smart
<p>@Roy_Smart has helpfully answered the second part of the question, so I'll answer the first :)</p>
<h3>TL;DR</h3>
<p>Basically NASA just pasted a Rowland circle on the telescope with adjustments and other equipment like microshutters to make FORTIS.</p>
<h3>Longer answer:</h3>
<p>First, let's have a look at the inside of the telescope:</p>
<p>FORTIS sounding rocket optical layout from <a href="https://www.researchgate.net/publication/1815017_FORTIS_Pathfinder_to_the_lyman_continuum#pf4" rel="nofollow noreferrer">Researchgate.net - FORTIS Pathfinder to the Lyman continuum</a>:</p>
<p><a href="https://i.sstatic.net/56KYq.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/56KYq.png" alt="enter image description here" /></a></p>
<p>Now this may sound confusing, but there is actually a Rowland circle, just not shown properly in the 2D layout:</p>
<blockquote>
<p>Spectroscopic design in the far ultraviolet below Lyα demands a minimalist approach. The “two-bounce” prime focus designs of the HUT, OREFUS and FUSE observatories used <strong>relatively fast parabolic primary mirrors feeding the slit of a Rowland circle spectrograph</strong>. Although these two-bounce designs satisfy the requirement for efﬁciency they have poor off-axis spectral imaging performance. This is because fast focal ratios tend to increase the height of the astigmatic image, limiting the spatial resolution perpendicular to the dispersion. Astigmatism control is a major challenge in <strong>Rowland circle spectrographs</strong> and methods have been developed to eliminate it at select wavelengths, either by controlling the gratingﬁgure12or with holographic ruling methods.</p>
</blockquote>
<p>From here, we can deduce a Rowland circle spectrograph is being used.</p>
<blockquote>
<p>Noda ﬁrst wrote out in detail the general aberration theory for holographic gratings, and since then techniques to minimize spectroscopic aberration shave become increasingly sophisticated. They reached a new level when solutions were found that made it possible to control not only astigmatism but coma at the high ruling densities required for the FUSE mission. The high resolution holographic gratings recorded for the Cosmic Origins Spectrograph (COS – slated to have been ﬂown on the now canceled servicing mission 4 to HST) removed the spherical aberration with an aspherical grating ﬁgure along with a FUSE like aberration minimization solution. <strong>Recently developed numerically optimized solutions for two-bounce systems achieve excellent narrow band spectroscopic imaging with the grating used off the Rowland circle</strong>. An off-axis parabola design has a high enough spectral resolving power to cleanly separate the <span class="math-container">$O\; VI\; λλ1032 – 1037$</span> doublet over a 0.5° ﬁeld of view and yield <span class="math-container">$4 – 9′′$</span> of spatial resolution.</p>
</blockquote>
<p>Now according to the <a href="https://www.researchgate.net/publication/1747629_Project_Lyman" rel="nofollow noreferrer">Researchgate.net - FORTIS Instrument Summary</a>, there are definitely circles:</p>
<p><a href="https://i.sstatic.net/M0AHl.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/M0AHl.png" alt="enter image description here" /></a></p>
<p>Further proven by the overall design of FORTIS:</p>
<p><a href="https://i.sstatic.net/Mk8yH.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Mk8yH.png" alt="enter image description here" /></a></p>
<hr />
<h3>Mathematical explanation of Rowland circle</h3>
<p>From the previous research paper in a foonote:</p>
<blockquote>
<p>In a Rowland circle spectrograph all the rays at wavelengths satisfying the grating equation entering a slit placed on a circle, with diameter is equal to the radius of the concave grating, are diffracted to a tangential focus on the same circle</p>
</blockquote>
<p>For reference, here is the grating equation derivation from <a href="https://www.newport.com/n/diffraction-grating-physics" rel="nofollow noreferrer">Newport.com - Diffraction grating physics</a> and <a href="https://www.newport.com/n/the-grating-equation" rel="nofollow noreferrer">Newport.com - The Grating Equation</a>:</p>
<p>From:
<a href="https://i.sstatic.net/gS3My.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/gS3My.png" alt="enter image description here" /></a></p>
<blockquote>
<p><sup> Figure 2-2. Geometry of diffraction, showing planar wavefronts. Two parallel rays, labeled 1 and 2, are incident on the grating one groove spacing d apart and are in phase with each other at wavefront A. Upon diffraction, the principle of constructive interference implies that these rays are in phase at diffracted wavefront B if the difference in their path lengths, <span class="math-container">$d \sinα + d \sinβ$</span>, is an integral number of wavelengths; this in turn leads to the grating equation. [Huygens wavelets not shown.] </sup></p>
</blockquote>
<p>We can deduce:</p>
<p><span class="math-container">$$ m\lambda=d_G(\sin\alpha+\sin\beta_m) $$</span></p>

CC BY-SA 4.0
2022-09-13T12:36:00.683Z
2022-09-14T23:27:12.967Z
2022-09-14T23:27:12.967Z
DialFrost
<p>The NASA Goddard news item <a href="https://www.nasa.gov/feature/goddard/2019/nasa-to-demonstrate-new-star-watching-technology-with-thousands-of-tiny-shutters" rel="nofollow noreferrer">NASA to Demonstrate New Star-Watching Technology with Thousands of Tiny Shutters</a> says:</p>
<blockquote>
<p>The technology, called the <strong>Next-Generation Microshutter Array (NGMSA)</strong>, will fly for the first time on the <strong>Far-ultraviolet Off Rowland-circle Telescope for Imaging and Spectroscopy, or FORTIS</strong>, mission on October 27. The array includes 8,125 <strong>tiny shutters</strong>, each about the width of a human hair, <strong>that open and close as needed to focus on specific celestial objects.</strong></p>
</blockquote>
<p><strong>Question:</strong> What is an <em>&quot;Off <a href="https://en.wikipedia.org/wiki/X-ray_fluorescence#Monochromators" rel="nofollow noreferrer">Rowland-circle</a> Telescope&quot;?</em> Are there &quot;On Rowland-circle Telescope&quot; as well?</p>
<hr />
<p>And speaking of microshutters:</p>
<ul>
<li><a href="https://astronomy.stackexchange.com/q/33757/7982">How will microshutter arrays be used in the James Webb and future space telescopes?</a></li>
<li><a href="https://astronomy.stackexchange.com/q/38860/7982">How were &quot;microshutters&quot; or other multiplexed or multi-object techniques first used in Astronomical spectroscopy?</a></li>
</ul>

CC BY-SA 4.0
2019-10-24T04:02:03.513Z
["We present here a design for a new type of far ultraviolet spectrograph, one that is more sensitive,
covers wider fields, and can provide spectra and images of a large number of objects simultaneously, called the Farultraviolet Off Rowland-circle Telescope for Imaging and Spectroscopy (FORTIS)."](https://arxiv.org/abs/astro-ph/0407464)
Keith McClary
CC BY-SA 4.0
2019-10-25T03:38:47.303Z
note to self: Footnote in Section 3 in the [paper](https://arxiv.org/abs/astro-ph/0407464) linked in the comment above reminds us: "In a Rowland circle spectrograph all the rays at wavelengths satisfying the grating equation entering a slit placed on a circle, with diameter is equal to the radius of the concave grating, are diffracted to a tangential focus on the same circle." In this telescope the Rowland circle is rotated around the telescope's axis. I don't know if that makes it a "Rowland sphere" or a "Rowland torus" but I assume it's the latter.
uhoh
CC BY-SA 4.0
2022-09-13T15:05:27.477Z
@DialFrost I skimmed and upvoted, it's late here and I'll give it a thorough read tomorrow. As far as I can tell you've completely nailed it! I usually wait at least several days before accepting answers. *Thanks!*
uhoh
<observational-astronomy><spectroscopy><terminology><space-telescope><instruments>
What is an "Off Rowland-circle Telescope"? Are there "On Rowland-circle Telescope" as well?
uhoh
# What is an "Off Rowland-circle Telescope"? Are there "On Rowland-circle Telescope" as well?

(Asked by: username_0 on 2019-10-23)

The NASA Goddard news item [NASA to Demonstrate New Star-Watching Technology with Thousands of Tiny Shutters](https://www.nasa.gov/feature/goddard/2019/nasa-to-demonstrate-new-star-watching-technology-with-thousands-of-tiny-shutters) says:

> The technology, called the **Next-Generation Microshutter Array (NGMSA)**, will fly for the first time on the **Far-ultraviolet Off Rowland-circle Telescope for Imaging and Spectroscopy, or FORTIS**, mission on October 27. The array includes 8,125 **tiny shutters**, each about the width of a human hair, **that open and close as needed to focus on specific celestial objects.**

**Question:** What is an *"Off [Rowland-circle](https://en.wikipedia.org/wiki/X-ray_fluorescence#Monochromators) Telescope"?* Are there "On Rowland-circle Telescope" as well?

---

And speaking of microshutters:

* [How will microshutter arrays be used in the James Webb and future space telescopes?](https://astronomy.stackexchange.com/q/33757/7982)
* [How were "microshutters" or other multiplexed or multi-object techniques first used in Astronomical spectroscopy?](https://astronomy.stackexchange.com/q/38860/7982)

**Tags:** observational-astronomy, spectroscopy, terminology, space-telescope, instruments
> **Comments:**
> **username_1**: ["We present here a design for a new type of far ultraviolet spectrograph, one that is more sensitive, covers wider fields, and can provide spectra and images of a large number of objects simultaneously, called the Farultraviolet Off Rowland-circle Telescope for Imaging and Spectroscopy (FORTIS)."](https://arxiv.org/abs/astro-ph/0407464)  
> **username_0**: note to self: Footnote in Section 3 in the [paper](https://arxiv.org/abs/astro-ph/0407464) linked in the comment above reminds us: "In a Rowland circle spectrograph all the rays at wavelengths satisfying the grating equation entering a slit placed on a circle, with diameter is equal to the radius of the concave grating, are diffracted to a tangential focus on the same circle." In this telescope the Rowland circle is rotated around the telescope's axis. I don't know if that makes it a "Rowland sphere" or a "Rowland torus" but I assume it's the latter.  
> **username_0**: @DialFrost I skimmed and upvoted, it's late here and I'll give it a thorough read tomorrow. As far as I can tell you've completely nailed it! I usually wait at least several days before accepting answers. *Thanks!*  

---

## 2 answers

### Answer by username_2 on 2022-09-13. Score: 3

The term 'off-Rowland-circle **telescope**' is a bit awkward, I think normally we would call the arrangement of FORTIS an off-Rowland-circle spectrograph, and they probably just used the word 'telescope' to make their acronym sound better. If we're being pedantic, then I think everything before the primary focus would be the telescope, and everything after is the spectrograph.

There are certainly on-Rowland-circle spectrographs, it's the simplest type of reflective spectrograph, and the [FORTIS paper](https://arxiv.org/abs/astro-ph/0407464) linked above by @Keith McClary mentioned several: HUT, OREFUS and FUSE.

In terms of an off-Rowland-circle spectrograph, I think the footnote you mentioned on page 4 says it all:

> In a Rowland circle spectrograph all the rays at wavelengths satisfying the grating equation entering a slit placed on a circle, with
> diameter is equal to the radius of the concave grating, are diffracted to a tangential focus on the same circle.

This is in contrast to FORTIS, which has magnification. In the figure below, I've taken the optical layout from the
[FORTIS paper](https://arxiv.org/abs/astro-ph/0407464) and annotated it with an approximate Rowland circle in a bold black line. From this figure, we can see that the primary focus is inside the Rowland circle, and the secondary focus (at the detector) is outside the Rowland circle. For FORTIS to be a on-Rowland-circle spectrograph, both the primary and secondary focus need to be the same distance from the grating and on the Rowland circle.

[![FORTIS optical layout with annotated Rowland circle](https://i.sstatic.net/a1uxt.png)](https://i.sstatic.net/a1uxt.png)

> **Comments:**
> **username_0**: Thanks! Can you also address "What is an 'Off Rowland-circle ***Telescope***'"? Is it a  Rowland-circle spectrometer duct-taped to a telescope, or is there some telescopic nature to the Rowland-circle optical design, or something else entirely?  
> **username_2**: In my opinion, an off-Rowland-circle telescope is a bit of an awkward term that they probably used to make their acronym sound better. I haven't heard that term before, but I just took it to mean your former suggestion, a spectrometer duct taped to a telescope.  
> **username_3**: @RoySmart That is correct :P And yes they have to make their acronyms sound nice! :D  

---

### Answer by username_3 on 2022-09-13. Score: 2

@Roy\_Smart has helpfully answered the second part of the question, so I'll answer the first :)

### TL;DR

Basically NASA just pasted a Rowland circle on the telescope with adjustments and other equipment like microshutters to make FORTIS.

### Longer answer:

First, let's have a look at the inside of the telescope:

FORTIS sounding rocket optical layout from [Researchgate.net - FORTIS Pathfinder to the Lyman continuum](https://www.researchgate.net/publication/1815017_FORTIS_Pathfinder_to_the_lyman_continuum#pf4):

[![enter image description here](https://i.sstatic.net/56KYq.png)](https://i.sstatic.net/56KYq.png)

Now this may sound confusing, but there is actually a Rowland circle, just not shown properly in the 2D layout:

> Spectroscopic design in the far ultraviolet below Lyα demands a minimalist approach. The “two-bounce” prime focus designs of the HUT, OREFUS and FUSE observatories used **relatively fast parabolic primary mirrors feeding the slit of a Rowland circle spectrograph**. Although these two-bounce designs satisfy the requirement for efﬁciency they have poor off-axis spectral imaging performance. This is because fast focal ratios tend to increase the height of the astigmatic image, limiting the spatial resolution perpendicular to the dispersion. Astigmatism control is a major challenge in **Rowland circle spectrographs** and methods have been developed to eliminate it at select wavelengths, either by controlling the gratingﬁgure12or with holographic ruling methods.

From here, we can deduce a Rowland circle spectrograph is being used.

> Noda ﬁrst wrote out in detail the general aberration theory for holographic gratings, and since then techniques to minimize spectroscopic aberration shave become increasingly sophisticated. They reached a new level when solutions were found that made it possible to control not only astigmatism but coma at the high ruling densities required for the FUSE mission. The high resolution holographic gratings recorded for the Cosmic Origins Spectrograph (COS – slated to have been ﬂown on the now canceled servicing mission 4 to HST) removed the spherical aberration with an aspherical grating ﬁgure along with a FUSE like aberration minimization solution. **Recently developed numerically optimized solutions for two-bounce systems achieve excellent narrow band spectroscopic imaging with the grating used off the Rowland circle**. An off-axis parabola design has a high enough spectral resolving power to cleanly separate the $O\; VI\; λλ1032 – 1037$ doublet over a 0.5° ﬁeld of view and yield $4 – 9′′$ of spatial resolution.

Now according to the [Researchgate.net - FORTIS Instrument Summary](https://www.researchgate.net/publication/1747629_Project_Lyman), there are definitely circles:

[![enter image description here](https://i.sstatic.net/M0AHl.png)](https://i.sstatic.net/M0AHl.png)

Further proven by the overall design of FORTIS:

[![enter image description here](https://i.sstatic.net/Mk8yH.png)](https://i.sstatic.net/Mk8yH.png)

---

### Mathematical explanation of Rowland circle

From the previous research paper in a foonote:

> In a Rowland circle spectrograph all the rays at wavelengths satisfying the grating equation entering a slit placed on a circle, with diameter is equal to the radius of the concave grating, are diffracted to a tangential focus on the same circle

For reference, here is the grating equation derivation from [Newport.com - Diffraction grating physics](https://www.newport.com/n/diffraction-grating-physics) and [Newport.com - The Grating Equation](https://www.newport.com/n/the-grating-equation):

From:
[![enter image description here](https://i.sstatic.net/gS3My.png)](https://i.sstatic.net/gS3My.png)

> Figure 2-2. Geometry of diffraction, showing planar wavefronts. Two parallel rays, labeled 1 and 2, are incident on the grating one groove spacing d apart and are in phase with each other at wavefront A. Upon diffraction, the principle of constructive interference implies that these rays are in phase at diffracted wavefront B if the difference in their path lengths, $d \sinα + d \sinβ$, is an integral number of wavelengths; this in turn leads to the grating equation. [Huygens wavelets not shown.]

We can deduce:

$$ m\lambda=d\_G(\sin\alpha+\sin\beta\_m) $$


---

