<p>You are making life difficult for yourself. Make the image <em>be</em> the number of stars per pixel and make sure your pixels are big enough to contain say at least 10 stars in each pixel.</p>

<p>At that point you can assume you have <a href="https://en.wikipedia.org/wiki/Poisson_distribution" rel="nofollow">Poissonian statistics</a> where the variance is equal to the expectation value. To a first approximation, what you have observed is the most likely expectation value, so the "noise" is the square root of the variance, which is the square root of how many stars are in each pixel. Thus your signal-to-noise map is simply the square root of the number of stars per pixel.</p>

<p>It maybe that your map has been normalised to give number of stars per unit angular area of the pixel. In which case, simply multiply by the pixel area and then take the square root.</p>

CC BY-SA 3.0
2016-03-14T22:43:51.793Z
Thank you for your answer. To be honnest with you, this work is asked to my internship. Up to now, it will not be too difficult to script what I want, create a heatmap etc .. But make a S/N map, I really have no idea to do that. I will discuss tomorrow with my teacher and I will suggest your idea ^^
Essex
CC BY-SA 3.0
2016-03-14T22:06:27.637Z
2016-03-14T22:06:27.637Z
ProfRob
<p>Recently, I obtained my heatmap from a sky survey. But now, I'm trying to get a signal to noise map from my heatmap.</p>

<p>My heatmap looks like :</p>

<p><img src="https://i.sstatic.net/9o6g5.jpg" alt="enter image description here"></p>

<p>My colour bar indicates the number of stars per pixel (I assume, but I'm not totally sure).</p>

<p>There are several steps in order to get my "S/N" map, but firstly, I need to get mean value from pixels around pixel i. To do that, I must draw a circle around the pixel i (circle with a radius about 10 arcmin, for exemple).</p>

<p>To know where I am, that's to say on which pixel I'm working. I scripted a red cross which indicates the pixel. I want to determine the mean value around this cross for each pixel in the heatmap.</p>

<p>I searched on this website and I found this post: Get pixel value after a colormap. I think that it will be interesting in my case also.</p>

<p>But I really haven't an idea to script this. After that, I need to calculate lots of things like gaussian RMS etc .. but for that, it will be easier.</p>

<p>This is my script : </p>

<pre><code>    # -*- coding: utf-8 -*-
    #!/usr/bin/env python

    from astropy.io import fits
    from astropy.table import Table
    from astropy.table import Column
    from astropy.convolution import convolve, Gaussian2DKernel
    import numpy as np
    import scipy.ndimage as sp
    import matplotlib.pyplot as plt



            ###################################
            # Importation du fichier de champ #
            ###################################

    filename = '/home/valentin/Desktop/Field169_combined_final_roughcal.fits_traite_traiteXY_traiteXY_final'

    print 'Fichier en cours de traitement' + str(filename) + '\n'

    # Ouverture du fichier à l'aide d'astropy
    field = fits.open(filename)         

    # Lecture des données fits  
    tbdata = field[1].data             


            #######################################
            # Parametres pour la carte de densité #
            #######################################

    # Boite des étoiles bleues :
    condition_1 = np.bitwise_and(tbdata['g0-r0'] &gt; -0.5, tbdata['g0-r0'] &lt; 0.8 )    # Ne garder que les -0.4 &lt; (g-r)0 &lt; 0.8
    condition_final = np.bitwise_and(tbdata['g0'] &lt; 23.5, condition_1)      # Récupere les valeurs de 'g0' &lt; 23.5 dans les valeurs de blue_stars_X

    Blue_stars = tbdata[condition_final]

    RA_Blue_stars = Blue_stars['RA']                        # Récupere les valeurs de 'RA' associées aux étoiles bleues
    DEC_Blue_stars = Blue_stars['DEC']                      # Récupere les valeurs de 'DEC' associées aux étoiles bleues


    # Boite des étoiles tres bleues :
    condition_2 = np.bitwise_and(tbdata['g0-r0'] &gt; -0.5, tbdata['g0-r0'] &lt; 0.2 )
    condition_final2 = np.bitwise_and(tbdata['g0'] &lt; 23.5, condition_2)

    Very_Blue_stars = tbdata[condition_final2]

    RA_Very_Blue_stars = Very_Blue_stars['RA']                      # Récupere les valeurs de 'RA' associées aux étoiles bleues
    DEC_Very_Blue_stars = Very_Blue_stars['DEC']

    # ==&gt; La table finale avec le masque s'appelle Blue_stars &amp; Very_Blue_stars

            ##################################################################
            # Traçage des différents graphiques de la distribution d'étoiles #
            ##################################################################


    fig1 = plt.subplot(2,2,1)
    plt.plot(tbdata['g0-r0'], tbdata['g0'], 'r.', label=u'Etoiles du champ')
    plt.plot(Blue_stars['g0-r0'], Blue_stars['g0'], 'b.', label =u'Etoiles bleues')
    plt.plot(Very_Blue_stars['g0-r0'], Very_Blue_stars['g0'], 'k.', label =u'Etoiles tres bleues')
    plt.title('Diagramme Couleur-Magnitude')
    plt.xlabel('(g0-r0)')
    plt.ylabel('g0')
    plt.xlim(-1.5,2.5)
    plt.ylim(14,28)
    plt.legend(loc='upper left')
    plt.gca().invert_yaxis()

    fig1 = plt.subplot(2,2,2)
    plt.plot(RA_Blue_stars, DEC_Blue_stars, 'b.', label =u'Etoiles bleues', alpha=0.15)
    plt.title('Carte de distribution des etoiles bleues')
    plt.xlabel('RA')
    plt.ylabel('DEC')
    plt.legend(loc='upper left')

    fig1 = plt.subplot(2,2,3)
    plt.plot(RA_Very_Blue_stars, DEC_Very_Blue_stars, 'r.', label =u'Etoiles tres bleues',alpha=0.4)
    plt.title('Carte de distribution des etoiles tres bleues')
    plt.xlabel('RA')
    plt.ylabel('DEC')
    plt.legend(loc='upper left')

    fig1 = plt.subplot(2,2,4)
    plt.plot(RA_Blue_stars, DEC_Blue_stars, 'b.', label =u'Etoiles bleues', alpha=0.15)
    plt.plot(RA_Very_Blue_stars, DEC_Very_Blue_stars, 'r.', label =u'Etoiles tres bleues',alpha=0.4)
    plt.title('Carte de distribution des etoiles bleues et tres bleues')
    plt.xlabel('RA')
    plt.ylabel('DEC')
    plt.legend(loc='upper left')

            ######################################################################
            # Traçage des différents graphiques de la carte de densité d'étoiles #
            ######################################################################


    # Carte de densité des étoiles bleues pour 1 pixel de 1 arcmin^2 (bins = 180)

    X_Blue_stars = Blue_stars['X']
    Y_Blue_stars = Blue_stars['Y']

    heatmap, xedges, yedges = np.histogram2d(X_Blue_stars, Y_Blue_stars, bins=180) # bins de 180 car 3° de champ en RA = 180 arcmin de champ en RA
    extent = [xedges[0], xedges[-1], yedges[0], yedges[-1]]

    RotatePlot = sp.rotate(heatmap,90)

    plt.clf()
    #fig = plt.subplot(2,2,1)
    plt.imshow(RotatePlot, extent=extent, interpolation='none')
    plt.colorbar()
    plt.title('Carte de densite des etoiles bleues (non lisse)')
    plt.xlabel("X")
    plt.ylabel("Y")


    # Carte de densité lissée (par convolution avec une gaussienne 2 sigma) des étoiles bleues pour 1 pixel de 1 arcmin^2 (bins = 180)
    # ==&gt; Avec Astropy

    plt.clf()
    fig = plt.figure(1)
    smoothed_heatmap = plt.imshow(convolve(RotatePlot, Gaussian2DKernel(stddev=2)), interpolation='nearest')
    plt.colorbar()
    plt.plot(100,120,'rx', markeredgewidth=3, markersize=10)
    plt.title('Carte de densite des etoiles bleues lisse (astropy)')
    plt.xlabel("X (arcmin)")
    plt.ylabel("Y (arcmin)")
    plt.xlim(0,180)
    plt.ylim(0,180)
    print smoothed_heatmap.cmap(smoothed_heatmap.norm(X_Blue_stars[100],Y_Blue_stars[120]))

    #plt.savefig('/home/valentin/Desktop/Final.png')
    plt.show()

    print "Création du Diagramme"
</code></pre>

<star><sky-survey><python>
Create a signal to noise map from heatmap
Essex
# Create a signal to noise map from heatmap

(Asked by: username_0 on 2016-03-14)

Recently, I obtained my heatmap from a sky survey. But now, I'm trying to get a signal to noise map from my heatmap.
My heatmap looks like :

My colour bar indicates the number of stars per pixel (I assume, but I'm not totally sure).
There are several steps in order to get my "S/N" map, but firstly, I need to get mean value from pixels around pixel i. To do that, I must draw a circle around the pixel i (circle with a radius about 10 arcmin, for exemple).
To know where I am, that's to say on which pixel I'm working. I scripted a red cross which indicates the pixel. I want to determine the mean value around this cross for each pixel in the heatmap.
I searched on this website and I found this post: Get pixel value after a colormap. I think that it will be interesting in my case also.
But I really haven't an idea to script this. After that, I need to calculate lots of things like gaussian RMS etc .. but for that, it will be easier.
This is my script : 
    # -*- coding: utf-8 -*-
    #!/usr/bin/env python

    from astropy.io import fits
    from astropy.table import Table
    from astropy.table import Column
    from astropy.convolution import convolve, Gaussian2DKernel
    import numpy as np
    import scipy.ndimage as sp
    import matplotlib.pyplot as plt



            ###################################
            # Importation du fichier de champ #
            ###################################

    filename = '/home/valentin/Desktop/Field169_combined_final_roughcal.fits_traite_traiteXY_traiteXY_final'

    print 'Fichier en cours de traitement' + str(filename) + '\n'

    # Ouverture du fichier à l'aide d'astropy
    field = fits.open(filename)         

    # Lecture des données fits  
    tbdata = field[1].data             


            #######################################
            # Parametres pour la carte de densité #
            #######################################

    # Boite des étoiles bleues :
    condition_1 = np.bitwise_and(tbdata['g0-r0'] > -0.5, tbdata['g0-r0'] < 0.8 )    # Ne garder que les -0.4 < (g-r)0 < 0.8
    condition_final = np.bitwise_and(tbdata['g0'] < 23.5, condition_1)      # Récupere les valeurs de 'g0' < 23.5 dans les valeurs de blue_stars_X

    Blue_stars = tbdata[condition_final]

    RA_Blue_stars = Blue_stars['RA']                        # Récupere les valeurs de 'RA' associées aux étoiles bleues
    DEC_Blue_stars = Blue_stars['DEC']                      # Récupere les valeurs de 'DEC' associées aux étoiles bleues


    # Boite des étoiles tres bleues :
    condition_2 = np.bitwise_and(tbdata['g0-r0'] > -0.5, tbdata['g0-r0'] < 0.2 )
    condition_final2 = np.bitwise_and(tbdata['g0'] < 23.5, condition_2)

    Very_Blue_stars = tbdata[condition_final2]

    RA_Very_Blue_stars = Very_Blue_stars['RA']                      # Récupere les valeurs de 'RA' associées aux étoiles bleues
    DEC_Very_Blue_stars = Very_Blue_stars['DEC']

    # ==> La table finale avec le masque s'appelle Blue_stars & Very_Blue_stars

            ##################################################################
            # Traçage des différents graphiques de la distribution d'étoiles #
            ##################################################################


    fig1 = plt.subplot(2,2,1)
    plt.plot(tbdata['g0-r0'], tbdata['g0'], 'r.', label=u'Etoiles du champ')
    plt.plot(Blue_stars['g0-r0'], Blue_stars['g0'], 'b.', label =u'Etoiles bleues')
    plt.plot(Very_Blue_stars['g0-r0'], Very_Blue_stars['g0'], 'k.', label =u'Etoiles tres bleues')
    plt.title('Diagramme Couleur-Magnitude')
    plt.xlabel('(g0-r0)')
    plt.ylabel('g0')
    plt.xlim(-1.5,2.5)
    plt.ylim(14,28)
    plt.legend(loc='upper left')
    plt.gca().invert_yaxis()

    fig1 = plt.subplot(2,2,2)
    plt.plot(RA_Blue_stars, DEC_Blue_stars, 'b.', label =u'Etoiles bleues', alpha=0.15)
    plt.title('Carte de distribution des etoiles bleues')
    plt.xlabel('RA')
    plt.ylabel('DEC')
    plt.legend(loc='upper left')

    fig1 = plt.subplot(2,2,3)
    plt.plot(RA_Very_Blue_stars, DEC_Very_Blue_stars, 'r.', label =u'Etoiles tres bleues',alpha=0.4)
    plt.title('Carte de distribution des etoiles tres bleues')
    plt.xlabel('RA')
    plt.ylabel('DEC')
    plt.legend(loc='upper left')

    fig1 = plt.subplot(2,2,4)
    plt.plot(RA_Blue_stars, DEC_Blue_stars, 'b.', label =u'Etoiles bleues', alpha=0.15)
    plt.plot(RA_Very_Blue_stars, DEC_Very_Blue_stars, 'r.', label =u'Etoiles tres bleues',alpha=0.4)
    plt.title('Carte de distribution des etoiles bleues et tres bleues')
    plt.xlabel('RA')
    plt.ylabel('DEC')
    plt.legend(loc='upper left')

            ######################################################################
            # Traçage des différents graphiques de la carte de densité d'étoiles #
            ######################################################################


    # Carte de densité des étoiles bleues pour 1 pixel de 1 arcmin^2 (bins = 180)

    X_Blue_stars = Blue_stars['X']
    Y_Blue_stars = Blue_stars['Y']

    heatmap, xedges, yedges = np.histogram2d(X_Blue_stars, Y_Blue_stars, bins=180) # bins de 180 car 3° de champ en RA = 180 arcmin de champ en RA
    extent = [xedges[0], xedges[-1], yedges[0], yedges[-1]]

    RotatePlot = sp.rotate(heatmap,90)

    plt.clf()
    #fig = plt.subplot(2,2,1)
    plt.imshow(RotatePlot, extent=extent, interpolation='none')
    plt.colorbar()
    plt.title('Carte de densite des etoiles bleues (non lisse)')
    plt.xlabel("X")
    plt.ylabel("Y")


    # Carte de densité lissée (par convolution avec une gaussienne 2 sigma) des étoiles bleues pour 1 pixel de 1 arcmin^2 (bins = 180)
    # ==> Avec Astropy

    plt.clf()
    fig = plt.figure(1)
    smoothed_heatmap = plt.imshow(convolve(RotatePlot, Gaussian2DKernel(stddev=2)), interpolation='nearest')
    plt.colorbar()
    plt.plot(100,120,'rx', markeredgewidth=3, markersize=10)
    plt.title('Carte de densite des etoiles bleues lisse (astropy)')
    plt.xlabel("X (arcmin)")
    plt.ylabel("Y (arcmin)")
    plt.xlim(0,180)
    plt.ylim(0,180)
    print smoothed_heatmap.cmap(smoothed_heatmap.norm(X_Blue_stars[100],Y_Blue_stars[120]))

    #plt.savefig('/home/valentin/Desktop/Final.png')
    plt.show()

    print "Création du Diagramme"

**Tags:** star, sky-survey, python

---

## 1 answers

### Answer by username_1 on 2016-03-14. Score: 1

You are making life difficult for yourself. Make the image *be* the number of stars per pixel and make sure your pixels are big enough to contain say at least 10 stars in each pixel.

At that point you can assume you have [Poissonian statistics](https://en.wikipedia.org/wiki/Poisson_distribution) where the variance is equal to the expectation value. To a first approximation, what you have observed is the most likely expectation value, so the "noise" is the square root of the variance, which is the square root of how many stars are in each pixel. Thus your signal-to-noise map is simply the square root of the number of stars per pixel.

It maybe that your map has been normalised to give number of stars per unit angular area of the pixel. In which case, simply multiply by the pixel area and then take the square root.

> **Comments:**
> **username_0**: Thank you for your answer. To be honnest with you, this work is asked to my internship. Up to now, it will not be too difficult to script what I want, create a heatmap etc .. But make a S/N map, I really have no idea to do that. I will discuss tomorrow with my teacher and I will suggest your idea ^^  

---

