| Re: PSF Energy inside circle [message #61576] |
Wed, 23 July 2008 13:52  |
wlandsman
Messages: 743
Registered: June 2000
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Senior Member |
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On Jul 23, 2:03 pm, Michael Aye <kmichael....@googlemail.com> wrote:
> Dear all,
> So how could I find and integrate the next "ring" of pixels? How would
> I even calculate the ever growing circumference correctly, taking into
> account that I have to sum up ever more pixels?
The options mentioned so far seem fine for large radii. For small
radii, the use of integer pixel values can introduce "noise" since a
pixel must be either entirely within or outside the circle. The
program aper.pro
( http://idlastro.gsfc.nasa.gov/ftp/pro/idlphot/aper.pro )
sums using partial pixels, using the exact overlap area of a pixel
with a circle.
The program is somewhat awkward to use, in part because it is very
old, and in part because it propagates error sources. But if you
want to compute the flux within 10 concentric circles centered at the
position [500.2, 500.5] with radii of 3, 3.5, 4, 4.5, ... 7.5 then the
following is a start:
IDL> apr = 3. + findgen(10)/2.
IDL> aper,im, 500.2, 500.5, flux, eflux, sky,skyerr, 1, apr,/
flux,setsky=0
IDL> plot, apr, flux ;plot encircled flux vs. radius
In this case I force the "sky" (background) to have a value of
zero. You can have aper.pro compute the background by giving it an
inner and outer "sky" radii far from the central source. --Wayne
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| Re: PSF Energy inside circle [message #61577 is a reply to message #61576] |
Wed, 23 July 2008 13:24  |
pgrigis
Messages: 436
Registered: September 2007
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Senior Member |
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Kenneth P. Bowman wrote:
> In article
> <8d5ea067-169e-4967-b3d9-29c2e14cf27e@f63g2000hsf.googlegroups.com>,
> Michael Aye <kmichael.aye@googlemail.com> wrote:
>
>> Dear all,
>> as so often I am either too blind to find existing stuff or puzzled
>> (if non-existing), that nobody did before what looks like a very usual
>> task.
>> What I want to know:
>> Where in an image array (usual 2d-array with values, e.g. a CCD image)
>> containing a centered 2d-gaussian light pulse lies the circle that
>> contains 80 % (for example) of the "energy" of all the light on the
>> image? I even only need it for the ideal situation where the center of
>> the CCD aligns with the center of the 2d-gaussian light distribution.
>> What I did so far:
>> - Collected useful procedures like psf_gaussian, dist_circle and
>> tvcircle.
>> - Found the algorithm how to integrate from the center pixel towards
>> outside, summing up the frame of pixels next to the previous frame. So
>> my cumulative sum contains the sum of the date of 1, 9, 25 ... pixels.
>>
>> But I would like to go in circles, not squares! :)
>> So how could I find and integrate the next "ring" of pixels? How would
>> I even calculate the ever growing circumference correctly, taking into
>> account that I have to sum up ever more pixels?
>> Sounds like a horrible coding work and I am hoping somebody did all
>> that already, because somehow that is something one would need to see
>> how good an optical PSF is, or not?
>>
>> As usual, I am grateful for any help or hint to literature, procedures
>> or calibration data of other experiments that might have done the
>> same.
>> Best regards,
>> Michael
>
> Compute the x and y coordinates of each pixel.
>
> x = REBIN(FINDGEN(nx), nx, ny)
> y = REBIN(REFORM(FINDGEN(ny), 1, ny), nx, ny)
>
> You might want to add 0.5 to locate the pixel centers.
>
> Compute the distance from each pixel to the central pixel
>
> d = SQRT((x - x0)^2 + (y - y0)^2)
>
> Then find rings like this
>
> i = WHERE((d GE d1) AND (d LE d2), count)
>
> Do what you want with those pixels.
Well, if one wants to use that strategy, I suggest
another option for finding out the radial behaviour:
-convert x,y cartesian coordinates of all pixels to r,phi in polar
coordinates
-interpolate the irregular r, phi values grid to a regular r, phi grid
-integrate (i.e. sum) the values with constant r for all r
-plot that as a function of r
That should nicely show the radial dependence of the psf...
Ciao,
Paolo
>
> You can put the WHERE statement in a loop and increment
> d1 and d2 over whatever values you want.
>
> Ken Bowman
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| Re: PSF Energy inside circle [message #61578 is a reply to message #61577] |
Wed, 23 July 2008 12:17 |
Kenneth P. Bowman
Messages: 585
Registered: May 2000
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Senior Member |
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In article
<8d5ea067-169e-4967-b3d9-29c2e14cf27e@f63g2000hsf.googlegroups.com>,
Michael Aye <kmichael.aye@googlemail.com> wrote:
> Dear all,
> as so often I am either too blind to find existing stuff or puzzled
> (if non-existing), that nobody did before what looks like a very usual
> task.
> What I want to know:
> Where in an image array (usual 2d-array with values, e.g. a CCD image)
> containing a centered 2d-gaussian light pulse lies the circle that
> contains 80 % (for example) of the "energy" of all the light on the
> image? I even only need it for the ideal situation where the center of
> the CCD aligns with the center of the 2d-gaussian light distribution.
> What I did so far:
> - Collected useful procedures like psf_gaussian, dist_circle and
> tvcircle.
> - Found the algorithm how to integrate from the center pixel towards
> outside, summing up the frame of pixels next to the previous frame. So
> my cumulative sum contains the sum of the date of 1, 9, 25 ... pixels.
>
> But I would like to go in circles, not squares! :)
> So how could I find and integrate the next "ring" of pixels? How would
> I even calculate the ever growing circumference correctly, taking into
> account that I have to sum up ever more pixels?
> Sounds like a horrible coding work and I am hoping somebody did all
> that already, because somehow that is something one would need to see
> how good an optical PSF is, or not?
>
> As usual, I am grateful for any help or hint to literature, procedures
> or calibration data of other experiments that might have done the
> same.
> Best regards,
> Michael
Compute the x and y coordinates of each pixel.
x = REBIN(FINDGEN(nx), nx, ny)
y = REBIN(REFORM(FINDGEN(ny), 1, ny), nx, ny)
You might want to add 0.5 to locate the pixel centers.
Compute the distance from each pixel to the central pixel
d = SQRT((x - x0)^2 + (y - y0)^2)
Then find rings like this
i = WHERE((d GE d1) AND (d LE d2), count)
Do what you want with those pixels.
You can put the WHERE statement in a loop and increment
d1 and d2 over whatever values you want.
Ken Bowman
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| Re: PSF Energy inside circle [message #61579 is a reply to message #61578] |
Wed, 23 July 2008 11:15 |
pgrigis
Messages: 436
Registered: September 2007
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Senior Member |
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Seems like a good situation for fitting a 2d gaussian peak to the
data.... This way you get all the parameters (intensity, FWHM)
directly...
Ciao,
Paolo
Michael Aye wrote:
> Dear all,
> as so often I am either too blind to find existing stuff or puzzled
> (if non-existing), that nobody did before what looks like a very usual
> task.
> What I want to know:
> Where in an image array (usual 2d-array with values, e.g. a CCD image)
> containing a centered 2d-gaussian light pulse lies the circle that
> contains 80 % (for example) of the "energy" of all the light on the
> image? I even only need it for the ideal situation where the center of
> the CCD aligns with the center of the 2d-gaussian light distribution.
> What I did so far:
> - Collected useful procedures like psf_gaussian, dist_circle and
> tvcircle.
> - Found the algorithm how to integrate from the center pixel towards
> outside, summing up the frame of pixels next to the previous frame. So
> my cumulative sum contains the sum of the date of 1, 9, 25 ... pixels.
>
> But I would like to go in circles, not squares! :)
> So how could I find and integrate the next "ring" of pixels? How would
> I even calculate the ever growing circumference correctly, taking into
> account that I have to sum up ever more pixels?
> Sounds like a horrible coding work and I am hoping somebody did all
> that already, because somehow that is something one would need to see
> how good an optical PSF is, or not?
>
> As usual, I am grateful for any help or hint to literature, procedures
> or calibration data of other experiments that might have done the
> same.
> Best regards,
> Michael
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| Re: PSF Energy inside circle [message #61664 is a reply to message #61578] |
Thu, 24 July 2008 05:43 |
Bob[3]
Messages: 60
Registered: December 2006
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Member |
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On Jul 23, 3:17 pm, "Kenneth P. Bowman" <k-bow...@null.edu> wrote:
> In article
> < 8d5ea067-169e-4967-b3d9-29c2e14cf...@f63g2000hsf.googlegroup s.com >,
> Michael Aye <kmichael....@googlemail.com> wrote:
>
>
>
>
>
>> Dear all,
>> as so often I am either too blind to find existing stuff or puzzled
>> (if non-existing), that nobody did before what looks like a very usual
>> task.
>> What I want to know:
>> Where in an image array (usual 2d-array with values, e.g. a CCD image)
>> containing a centered 2d-gaussian light pulse lies the circle that
>> contains 80 % (for example) of the "energy" of all the light on the
>> image? I even only need it for the ideal situation where the center of
>> the CCD aligns with the center of the 2d-gaussian light distribution.
>> What I did so far:
>> - Collected useful procedures like psf_gaussian, dist_circle and
>> tvcircle.
>> - Found the algorithm how to integrate from the center pixel towards
>> outside, summing up the frame of pixels next to the previous frame. So
>> my cumulative sum contains the sum of the date of 1, 9, 25 ... pixels.
>
>> But I would like to go in circles, not squares! :)
>> So how could I find and integrate the next "ring" of pixels? How would
>> I even calculate the ever growing circumference correctly, taking into
>> account that I have to sum up ever more pixels?
>> Sounds like a horrible coding work and I am hoping somebody did all
>> that already, because somehow that is something one would need to see
>> how good an optical PSF is, or not?
>
>> As usual, I am grateful for any help or hint to literature, procedures
>> or calibration data of other experiments that might have done the
>> same.
>> Best regards,
>> Michael
>
> Compute the x and y coordinates of each pixel.
>
> x = REBIN(FINDGEN(nx), nx, ny)
> y = REBIN(REFORM(FINDGEN(ny), 1, ny), nx, ny)
>
> You might want to add 0.5 to locate the pixel centers.
>
> Compute the distance from each pixel to the central pixel
>
> d = SQRT((x - x0)^2 + (y - y0)^2)
>
> Then find rings like this
>
> i = WHERE((d GE d1) AND (d LE d2), count)
>
> Do what you want with those pixels.
>
> You can put the WHERE statement in a loop and increment
> d1 and d2 over whatever values you want.
>
> Ken Bowman- Hide quoted text -
>
> - Show quoted text -
Is there an advantage of using this method to determine d over using
DIST?
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| Re: PSF Energy inside circle [message #61708 is a reply to message #61664] |
Fri, 25 July 2008 10:18 |
Kenneth P. Bowman
Messages: 585
Registered: May 2000
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Senior Member |
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In article
<808314ce-4419-478d-8593-bc94dd7f1789@p25g2000hsf.googlegroups.com>,
Bob Crawford <Snowman42@gmail.com> wrote:
> Is there an advantage of using this method to determine d over using
> DIST?
DIST computes a different function.
!P.MULTI = [0, 2, 1]
x = FINDGEN(51)
xx = REBIN(x, 51, 51)
yy = REBIN(REFORM(x, 1, 51), 51, 51)
d = SQRT((xx - 25.0)^2 + (yy - 25.0)^2)
SURFACE, d
SURFACE, DIST(51)
The Euclidian distance is a circular cone. DIST computes an
array proportional to the frequency of each element.
Ken Bowman
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| Re: PSF Energy inside circle [message #61751 is a reply to message #61708] |
Tue, 29 July 2008 08:38 |
Bob[3]
Messages: 60
Registered: December 2006
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Member |
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On Jul 25, 1:18 pm, "Kenneth P. Bowman" <k-bow...@null.edu> wrote:
> In article
> < 808314ce-4419-478d-8593-bc94dd7f1...@p25g2000hsf.googlegroup s.com >,
> Bob Crawford <Snowma...@gmail.com> wrote:
>
>> Is there an advantage of using this method to determine d over using
>> DIST?
>
> DIST computes a different function.
>
> !P.MULTI = [0, 2, 1]
> x = FINDGEN(51)
> xx = REBIN(x, 51, 51)
> yy = REBIN(REFORM(x, 1, 51), 51, 51)
> d = SQRT((xx - 25.0)^2 + (yy - 25.0)^2)
> SURFACE, d
> SURFACE, DIST(51)
>
> The Euclidian distance is a circular cone. DIST computes an
> array proportional to the frequency of each element.
>
> Ken Bowman
Thank you - but I was referring to the simplified situation as
described in this post:
http://groups.google.ca/group/comp.lang.idl-pvwave/browse_th read/thread/69b7be558f84e5be/2c185f37b1f50503?hl=en&lnk= gst#2c185f37b1f50503
i.e. replace:
SURFACE, DIST(51)
with:
SURFACE, SHIFT(DIST(51),25,25)
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| Re: PSF Energy inside circle [message #61813 is a reply to message #61578] |
Wed, 30 July 2008 15:06 |
maye
Messages: 29
Registered: June 2006
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Junior Member |
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On Jul 23, 9:17 pm, "Kenneth P. Bowman" <k-bow...@null.edu> wrote:
> In article
> < 8d5ea067-169e-4967-b3d9-29c2e14cf...@f63g2000hsf.googlegroup s.com >,
> Michael Aye <kmichael....@googlemail.com> wrote:
>
>
>
>> Dear all,
>> as so often I am either too blind to find existing stuff or puzzled
>> (if non-existing), that nobody did before what looks like a very usual
>> task.
>> What I want to know:
>> Where in an image array (usual 2d-array with values, e.g. a CCD image)
>> containing a centered 2d-gaussian light pulse lies the circle that
>> contains 80 % (for example) of the "energy" of all the light on the
>> image? I even only need it for the ideal situation where the center of
>> the CCD aligns with the center of the 2d-gaussian light distribution.
>> What I did so far:
>> - Collected useful procedures like psf_gaussian, dist_circle and
>> tvcircle.
>> - Found the algorithm how to integrate from the center pixel towards
>> outside, summing up the frame of pixels next to the previous frame. So
>> my cumulative sum contains the sum of the date of 1, 9, 25 ... pixels.
>
>> But I would like to go in circles, not squares! :)
>> So how could I find and integrate the next "ring" of pixels? How would
>> I even calculate the ever growing circumference correctly, taking into
>> account that I have to sum up ever more pixels?
>> Sounds like a horrible coding work and I am hoping somebody did all
>> that already, because somehow that is something one would need to see
>> how good an optical PSF is, or not?
>
>> As usual, I am grateful for any help or hint to literature, procedures
>> or calibration data of other experiments that might have done the
>> same.
>> Best regards,
>> Michael
>
> Compute the x and y coordinates of each pixel.
>
> x = REBIN(FINDGEN(nx), nx, ny)
> y = REBIN(REFORM(FINDGEN(ny), 1, ny), nx, ny)
>
> You might want to add 0.5 to locate the pixel centers.
>
> Compute the distance from each pixel to the central pixel
>
> d = SQRT((x - x0)^2 + (y - y0)^2)
>
> Then find rings like this
>
> i = WHERE((d GE d1) AND (d LE d2), count)
>
> Do what you want with those pixels.
>
> You can put the WHERE statement in a loop and increment
> d1 and d2 over whatever values you want.
>
I tried your method, it works fine, thanks!
A side question:
For a 1D Gaussian, 68 % of events/energy/.. lies insides 1 sigma, how
is this number for a 2D Gaussian? I have a hard time to find
statistical tables for 2D Gaussians? And is it possible to get that
number analytically?
Best regards,
Michael
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