Hi John,
You may already know this but I just explored the relationship between the latest PSF Signal weights and NWEIGHT. PSF Signal Power is more closely correlated with NWEIGHT. This is using data from the Witch Head nebula dataset referenced in
this message (with corrections to my interpretation in my followup message there).
John
| PSF Signal Weight | PSF Signal Power Weight |
Correlation with NWEIGHT | 0.9333 | 0.9826 |
Variance in NWEIGHT Explained by | 0.8702 | 0.9652 |
View attachment 13066View attachment 13067
Thanks, an interesting analysis of NWEIGHT and PSF weights (PixInsight -12 versions).
The NormalizeScaleGradient NWEIGHT has a single goal - to optimize the signal to noise ratio (the reason I concentrate on this single measure is explained here:
https://pixinsight.com/forum/index.php?threads/subframeselector-evaluation.17696/post-107507 . Note that there are situations where you might want a weight to depend on star profiles. See
https://pixinsight.com/forum/index.php?threads/subframeselector-evaluation.17696/post-107511 ).
The NSG algorithm is based on the physics. Provided that the noise is dominated by shot noise, it will work in all situations (the physics does not change).
- NSG determines the astronomical signal directly from stellar photometry. Note that by measuring the astronomical signal in this way, it excludes light pollution, which would invalidate the result.
- It uses the PixInsight calculated noise estimate, derived from calibrated but unregistered images. It is really important that the noise estimate was from unregistered images, because registration has a smoothing effect on the noise which is not consistent between images.
- NWEIGHT is then the square of the signal to noise ratio: ((Astronomical signal)/(PixInsight noise estimate))^2.
You can check that the square of the signal to noise ratio works with the following thought experiment:
- Take a 1 minute and 4 minute exposure in identical conditions.
- The relative signal to noise ratio of each image will be the square root of the exposure time (1 and 2). This relationship holds true provided that the noise is dominated by shot noise.
- We calculate the weight by squaring the signal to noise ratio. We then get weights of 1 and 4. We can see that this is correct. The 4 minute exposure must be worth four times as much as the 1 minute exposure.
The NWEIGHT accuracy depends upon the PixInsight noise estimate, and the accuracy of the stellar photometry. The stellar photometry is performed on registered images, which has the advantage that we can be sure we are comparing the same stars in the reference and target images. However, the disadvantage is that the registration process will not fully conserve star flux, which will introduce an error. Is this error significant?
The best way to test this is to take exposures of different length in identical conditions. From the thought experiment, it can be shown that the noise should be proportional to the square root of the exposure time ratio. The signal should be proportional to the exposure time. If the signal error is smaller than the noise error, then using registered images is OK. My own tests indicate that it is OK, but you should perform your own tests. NSG writes the calculated scale factor to the FITS header NSGS0, NSGS1 and NSGS2. The PixInsight noise estimate: NOISE00, NOISE01, NOISE02. You can extract these header values using Blink statistics.
The PSF weights are calculated using a very different strategy and use different algorithms. I would therefore expect the relationship between PSFSignalPower and NWEIGHT to depend on the data set. PixInsight has always tried to provide the user with plenty of choice. Once PixInsight -12 is released, you will be able to choose from 3 different algorithms (PSFSignalWeight, PSFSignalPowerWeight, NWEIGHT), which must be a good thing.