Is drizzle2x then downsampled helping?

Andrea and Brian are correct you are under-sampled, you can see it visually, or as Brian mentioned, from your plate scale. Under-sampled is where a 2X drizzle would help your image with a better-defined point spread function and improved resolution. So understanding how much drizzle is helping you is an important question.

The main issue I see with your analysis is that you have not chosen the right kind of image for this comparison and you have done too much to the image before trying to do this analysis.

You should choose an image or a part of an image that has mostly medium bright stars and not many bright saturated stars, and preferably no nebulosity or elliptical galaxies that might be confused as stars. This is image is totally washing out the stars, so fitting these stars to any model is very problematic.

Also, I would fit way less stars, you want to look at the medium brightness stars and not pick up too many faint ones. You probably have more than 10X too many stars counted, likely some of these stars are just noise. It also is a good idea to use the centre of a FOV if there are any aberrations away from the center of the frame.

In processing to find the impact of drizzle, treat your image with care, do only calibrations, background correction and a simple and non-aggressive stretch. An image with medium bright stars, like a distant open cluster that is well resolved would be perfect, and doesn’t require a strong stretch which can distort the psf, and will provide good contrast and S/N. You did BXT on these images, that changes star shapes, you want to be working on as natural a psf as you can, so do not do any sort of star shaping processing or even deconvolution, work with the least manipulation of the data.

Finally, for the drizzled data, it appears you ran it on the downscaled image. Instead, run it on the drizzled image. Any pixel values can be divided by 2 to compare, other values are not going to change. Again, you are manipulating the result after the drizzle, which can affect the result.

In other words, drizzle impacts your raw image quality, you want to keep it as close as possible to that to understand the improvement. And with a better image quality with drizzle your entire further processing workflow will need to be adjusted.

Now, while the data here is not suitable for a proper analysis due to the issues above, here is the sort of analysis you need to do.

You need to find what is the correct model for your psf. The usual psf when viewed from earth is a Moffat distribution, which is somewhere between Gaussian and Lorentzian, though one should remember that any of the distributions are an approximation. Lorentzian’s give a narrower peak, but then have a wide base or wings, which Gaussian’s do not have. This means that the fit of a Lorentzian depends on these fainter wings, which are noisier. So if your S/N is not great the Lorentzian fit can be problematic.

Now you fitted both models to the data, the question you should ask the model results is which model is most accurate to fit your data. That is the model you should use. Again, though neither a Gaussian or a Lorentzian is likely going to be best of all models, there is likely a Moffat that is better.

So let’s look at the model quality as an illustration. We will ignore small changes as they are affected by noise.

The median residual is the median value of the deviations from the model in DN or ADU units, so how much the intensity in the model deviates from the data. The MAD FWHM is the variance of the FWHM data from the model in pixels, and the MAD residual is the variance of the residual deviations from the model, so again the variance to the model of the intensities in the data psf.

As you can see, there is a huge difference in two of these metrics, with the Lorentzian model not fitting the data anywhere near as well as the Gaussian. With both models the fit of the data to the model improves with drizzle. So if we take all this at face value the Gaussian model is much better and drizzle gives a better fit to the data. Because you are under-sampled originally, there are few pixels to define the stars (except for the very bright ones which are spread out over more pixels), thus the model before drizzle has a hard time fitting the data. More pixels after drizzle gives more precision to the data and thus to the model. When you see the model improve this dramatically you know that you were under-sampled, and to this extent at least, drizzle is helping no matter what model you base it on—your data is now more precise.

Again, due to the problems I outlined, the small differences in FWHM etc are surely just noise.

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Personally, in my own setup I am close to being sampled correctly by theory. However, I always notice an improvement in FWHM with drizzle. If you are under-sampled, there should be a significant difference with FWHM on drizzle, I think suitable data and processing will show that for you.

I hope this helps you see what needs to be done to choose a model and then to ask questions whether drizzle helps.

Rick

Theory says that drizzle offers the optimal S/N ratio.

The idea that the signal from one pixel is divided over more than one pixel, so therefore S/N goes down is too simplistic. The thing is that the dithering results in correlation of signals over the new nearby pixels, which means the noise in those new pixels is also correlated. Essentially there is averaging over pixels (that is different pixels contribute to the final pixels, which reduces the overall noise.

Note all this assumes good dithering, no dithering and drizzle doesn’t work properly.

The other point is that the noise is finer grain after drizzle, just as the signal is finer grain. This makes the noise less objectionable, the finer the noise the less we are able to see it. Also, the finer the noise, the easier to use noise reduction at smaller scales. The psf covers 4X the pixels with a 2X drizzle, so noise size in pixels is smaller relative to the psf. Thus, easier to use noise reduction without broadening the psf.

I think since you are very undersampled I would leave it at 2X, not down sample—the stars are going to look so much nicer that it will be much more appealing. There is more to S/N than just the numbers.

Rick

At the risk of repeating what you already know, I would like to add a couple of bits to others’, already useful, answers.

I always run DrizzleIntegration manually. On one hand I want to control the process and determine the parameters myself, on the other hand it cements my understanding of the process.

The drizzle scale (2x, 3x, etc.) depends on the FWHM as measured on calibrated frames. But as seeing impacts FWHM and my seeing varies (between sessions & during the night), I measure FWHM for a set of frames (SubframeSelector or DynamicPSF) and take the median value.

• With FWHM < 2.5px, drizzle is highly recommended

• When FWHM between 2.5px and 3px, drizzle is recommended

• With FWHM > 3px, drizzle won’t provide sampling improvements but is still useful for integration without interpolation (i.e. with OSC)

Having the FWHM measured you can use a formula to determine the right scale. You can look the details in DrizzleIntegration’s documentation but generally it boils down to \(ceil(3/FWHM)\).

The rest of the DrizzleIntegration parameters, such as Drop Shrink and kernel function, I determine by testing. Enabling Fast Drizzle and using a ROI significantly speed up the process. After each run, I check the resulting drizzle_weights map where:

• I apply boosted STF and inspect the map for consistency i.e. no “blotches”

• I use Statistics to check coverage (mean, minimum and maximum values). Higher values are better.

I hope this is useful to you.

Clear skies

Nope, they were correct as stated.

This is an interesting discussion and love it! I always had these kind of question but was never understood myself and hence was not sure how to put it in front to ask!

Thank you guys!