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I think to measure guiding quality you need to take several very short exposures (or measure many stars in a single short exposure) to get an average "short-exposure FWHM". This short-exposure FWHM is the baseline against which you can measure autoguider performance by comparing it to the average FWHM you get in a longer duration autoguided exposure. How little the FWHM increases I think would be the most accurate determination of autoguiding quality. But even in this case seeing can be an unknown factor so it's important to average many stars.

-Ray Gralak

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The complication is that in short (focus) exposures, the FWHM estimates can be inaccurate as the stars can be quite non-Gaussian. Most astro-software rely on Gaussian fit to get FWHM and centroid. Also during a long-exposure, the local seeing could actually improve compared to the (earlier) short exposure. So I am not so sure if the short-exposure is a good baseline to quantify guiding quality.

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Does it really make sense to measure autoguiding with 3-5 arc-second/pixel image scale? Of course you want to have an image scale at least 1 arc-sec/pixel for doing these types of meanurements.

-Ray

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Does it really make sense to measure autoguiding with 3-5 arc-second/pixel image scale? Of course you want to have an image scale at least 1 arc-sec/pixel for doing these types of meanurements.

-Ray

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Does it really make sense to measure autoguiding with 3-5 arc-second/pixel image scale? Of course you want to have an image scale at least 1 arc-sec/pixel for doing these types of meanurements.

-Ray

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Huh? How did I imply that? I am not saying the stars are non-Guassian because of under sampling. Individual short-exposures can still be significantly non-Guassian at my pixel scale of 0.5"/px because of dispersion.
examples here

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And that's why I said you need to average many stars (or pick only "good" stars). Some stars are going to have better shapes than others. The idea is to get a BASELINE performance of the optics with minimal effects from seeing...

-Ray

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Does it really make sense to measure autoguiding with 3-5 arc-second/pixel image scale? Of course you want to have an image scale at least 1 arc-sec/pixel for doing these types of meanurements.

-Ray

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Huh? How did I imply that? I am not saying the stars are non-Guassian because of under sampling. Individual short-exposures can still be significantly non-Guassian at my pixel scale of 0.5"/px because of dispersion.
examples here

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And that's why I said you need to average many stars (or pick only "good" stars). Some stars are going to have better shapes than others. The idea is to get a BASELINE performance of the optics with minimal effects from seeing...

-Ray

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An example might help you understand what I mean... using the same scope one could do two long exposure images. One in focus, and the other out of focus. If the autoguider could be left in focus both images would theoretically have the same autoguiding quality however the one out of focus is going to have a much higher FWHM. So, it is important to have a baseline measurement of short exposure FWHM to measure against long exposure FWHM. That is, the higher FWHM is not because of poorer autoguiding. I've seen a few people try to say their autoguiding is better because their FWHM is tighter but that is an apples to oranges comparison. The measurement of autoguider performance in a long exposure should be related to the amount of degradation that occurs compared to a short exposure.

Hopefully this makes things clearer?

-Ray

Edited by Ray Gralak (01/01/13 01:17 PM)

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Having looked at PECPrep's source code I saw that it only uses FFTs, which are only fair approximations. PEMPRo uses FFTs to ballpark the frequencies but then PEMPRo uses much more advanced techniques to get the correct frequencies, amplitudes, and phases. PECPrep's values are probably higher because it is including noise that is removed via PEMPro's more advanced techniques.

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Having looked at PECPrep's source code I saw that it only uses FFTs, which are only fair approximations. PEMPRo uses FFTs to ballpark the frequencies but then PEMPRo uses much more advanced techniques to get the correct frequencies, amplitudes, and phases. PECPrep's values are probably higher because it is including noise that is removed via PEMPro's more advanced techniques.

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As you know every continuous periodic function can be expanded to Fourier series. FFT is a smart and efficient numerical algorithm that decomposes a sequence of values into components of different frequencies thus in essence it expands a periodic error curve (PEC) to Fourier series. This method is well established and reviewed by mathematicians and practitioners. DTF would be more accurate but more time consuming and there would be no practical difference. PEMPro, from what you said in the past, uses proprietary techniques that I am highly skeptical of. Publish your advanced techniques and let specialists review and approve them. In the meantime I will stick to PECPrep and FFT for PEC analysis.

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FFT's are old-school. The techniques are easily found if you do searches for them but I consider the specific methods PEMPro uses as trade secrets (and there will be advances in PEMPro V3). I can tell you the techniques used are related to singular value decomposition. Many tool vendors, include the PECPrep author has copied PEMPro's ideas so I'm not about to give people more things to copy.

-Ray

Edited by Ray Gralak (01/01/13 01:31 PM)

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i believe Frank has said as much...

compare FWHM of short (5 to 10 second) exposures with FWHM of long guided exposures, this will tell if the FWHM is atmosphere limited or mount limited..

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Frank's the major culprit to whom I was beating this point. I'm glad he finally accepted that.

-Ray

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Having looked at PECPrep's source code I saw that it only uses FFTs, which are only fair approximations. PEMPRo uses FFTs to ballpark the frequencies but then PEMPRo uses much more advanced techniques to get the correct frequencies, amplitudes, and phases. PECPrep's values are probably higher because it is including noise that is removed via PEMPro's more advanced techniques.

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As you know every continuous periodic function can be expanded to Fourier series. FFT is a smart and efficient numerical algorithm that decomposes a sequence of values into components of different frequencies thus in essence it expands a periodic error curve (PEC) to Fourier series. This method is well established and reviewed by mathematicians and practitioners. DTF would be more accurate but more time consuming and there would be no practical difference. PEMPro, from what you said in the past, uses proprietary techniques that I am highly skeptical of. Publish your advanced techniques and let specialists review and approve them. In the meantime I will stick to PECPrep and FFT for PEC analysis.

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I cannot understand how a well established and robust procedure (FFT) is not enough to model the relatively simple undulations of what we see in a mount periodic curve. FFT is used in complex DSP and spectrum analyzers for many hundreds of MHz of frequencies.

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Having looked at PECPrep's source code I saw that it only uses FFTs, which are only fair approximations. PEMPRo uses FFTs to ballpark the frequencies but then PEMPRo uses much more advanced techniques to get the correct frequencies, amplitudes, and phases. PECPrep's values are probably higher because it is including noise that is removed via PEMPro's more advanced techniques.

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As you know every continuous periodic function can be expanded to Fourier series. FFT is a smart and efficient numerical algorithm that decomposes a sequence of values into components of different frequencies thus in essence it expands a periodic error curve (PEC) to Fourier series. This method is well established and reviewed by mathematicians and practitioners. DTF would be more accurate but more time consuming and there would be no practical difference. PEMPro, from what you said in the past, uses proprietary techniques that I am highly skeptical of. Publish your advanced techniques and let specialists review and approve them. In the meantime I will stick to PECPrep and FFT for PEC analysis.

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BTW, how did you determine that PECPrep is even accurate? The critical FFT routines are NOT open source. For all you know there could be a bug. The author seems to have a standing policy of letting the users test his code rather than always doing it himself.

-Ray

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I'm not about to give people more things to copy.

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You can't stop people from using deobfuscators.

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BTW, how did you determine that PECPrep is even accurate? The critical FFT routines are NOT open source. For all you know there could be a bug. The author seems to have a standing policy of letting the users test his code rather than always doing it himself.

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I'm not about to give people more things to copy.

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You can't stop people from using deobfuscators.

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Good luck with that, Adam!

-Ray

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BTW, how did you determine that PECPrep is even accurate? The critical FFT routines are NOT open source. For all you know there could be a bug. The author seems to have a standing policy of letting the users test his code rather than always doing it himself.

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The reason I touched on this subject is that PEMPro results in too many misfits. I have seen it on my own and other data. On the other hand I compared many results from PECPrep to Software Bisque's PEC software and they were in a pretty good agreement. Looks like we are digressing from the OP's question so this will be my last comment.

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Show me!!

-Ray

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Having looked at PECPrep's source code I saw that it only uses FFTs, which are only fair approximations. PEMPRo uses FFTs to ballpark the frequencies but then PEMPRo uses much more advanced techniques to get the correct frequencies, amplitudes, and phases. PECPrep's values are probably higher because it is including noise that is removed via PEMPro's more advanced techniques.

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As you know every continuous periodic function can be expanded to Fourier series. FFT is a smart and efficient numerical algorithm that decomposes a sequence of values into components of different frequencies thus in essence it expands a periodic error curve (PEC) to Fourier series. This method is well established and reviewed by mathematicians and practitioners. DTF would be more accurate but more time consuming and there would be no practical difference. PEMPro, from what you said in the past, uses proprietary techniques that I am highly skeptical of. Publish your advanced techniques and let specialists review and approve them. In the meantime I will stick to PECPrep and FFT for PEC analysis.

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I cannot understand how a well established and robust procedure (FFT) is not enough to model the relatively simple undulations of what we see in a mount periodic curve. FFT is used in complex DSP and spectrum analyzers for many hundreds of MHz of frequencies.

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There's nothing seriously wrong with FFTs but I think if you did some research you would find that there are definitely disadvantages and limitations to FFTs. There are definitely better (i.e more accurate) methods employed today. PEMPro does use FFT's to approximate and identify frequencies but it uses more advanced methods to actually calculate the magnitudes, phases, and removing noise from the signal.

-Ray

Edited by Ray Gralak (01/01/13 03:08 PM)

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