This image compares the log magnitude spatial frequency spectrum of two images. The spectrum on the left corresponds to the RGB/H-alpha image of the Elephant Trunk from the Rowe, NM dark site that I uploaded a few days ago. The spectrum on the right corresponds to the RGB image of the Elephant Trunk that I just uploaded today, taken last night in my backyard.

The spectra have been scaled to correspond 1:1 in spatial frequency and in image intensity. It is clear that my image suffers compared to the Rowe, NM data. I can't yet describe why my vertical frequencies extend more than the horizontal frequencies. But the important thing is the fraction of the width / height occupied by the central disk of the spectra. The broader that central disk, extending closer to the edge of the image here, the better high spatial frequencies are retained in the image.

It is easy to see by eye when looking and comparing the two Elephant Trunk images. Our pixel scales on the sensor are about the same (2 arcsec / pix for Rowe, NM, and 1.79 arcsec / pixel for my backyard). The Rowe, NM site uses a monochrome detector, while I use an ATIK OSC with a Bayer matrix. The Rowe focal length is 450 mm, while my own C8 HyperStar is 425 mm (nearly the same).

The Bayer matrix surely accounts for some of the loss in spatial resolution. But I would argue too, that seeing conditions and sky background noise levels also act as low-pass filters. The seeing and sky background are significantly lower (i.e., much better) at Rowe, NM than in my own backyard.

There was a 2.5 mag sky background difference between us last night. Rowe, NM typically reports a sky background of 22 mag / arcsec^2, while, with the same meter to +/- 0.1 mag I reported 19.5 mag at the darkest period last night.

I can only guess at seeing conditions. If my star sizes are any indication, over a 180 sec integration period I averaged around 6 arcsec seeing, at best, and around 7 arcsec on average. (Yuk!)

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Revision corrected the aspect ratio thingy... both spectral images have a scale of 270 pix for frequencies ranging from -0.5 to +0.5 cycles / pixel, along both axes.

As expected they are symmetric in X and Y axes. But the conclusion from above still holds true: DSW has a better site than my backyard, and its spatial cutoff frequency is correspondingly higher than mine. That's why all the edge contrast shows up so much better in images from DSW.

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These images were generated by taking the FFT of the respective astro-images, then computing Log(x) - Log(Max(x)) on every pixel value, x, over the FFT images, and then normalizing their shapes to a square region. They show how much of the space of spectral frequency information is being used by the images. This also normalizes the images to ignore differences in signal levels and shows only how much of the spectral frequency space is being used, and to what degree.

In a perfect world, an image of a lone star would produce a disk image, brightest at the center and tapering off to the very edge of the image frame. [ the image would be the autocorrelation function of the illuminated aperture ] In such case we would be operating at our diffraction limit, set by the laws of physics and nature. But in the real world, other factors limit our ability to achieve that. Optical aberrations, atmospheric seeing conditions, and sky background noise, and sensor Bayer patterns, all act to shrink the ideal image into one of those shown above.

In the comparison between my backyard C8 HyperStar + ATIK 490 OSC against the Rowe, NM, Takehashi refractor, monochrome QSI camera system, there will be some effects caused by differences in our equipment. By normalizing these images to a square region, we largely remove differences in aperture size for this comparison. Larger apertures collect more light and have smaller diffraction limit (Airy disk size). But that has been normalized between us, so that we show only how much of the available information is being used.

Of course, my Bayer matrix sensor means that my true autocorrelation image will show regions of aliasing (bright areas near the corners and edges of the above frame). And so precautions have to eb applied during deBayering to filter away some of the aliased information. Ideally, we should have pre-filtered the light arriving at the sensor with anti-aliasing filters (Canon cameras do this), because once the light is sampled by the sensor, aliasing has already happened and you can't remove aliasing completely thereafter. But at any rate, my available information should have been limited to no more than half the square image size shown above -- and you pretty much see that.

That means that I should not be able to see structures very well when their spatial extent is smaller than 4 pixels across. And so for that reason alone, the QSI monochrome sensor could outperform my own.

okay.... so let's remove that first obvious difference between us. Let's downsample each astro-image by 2x2 and then redo the comparison -- latest revision now shows that situation. Now you still see that even at 2x2 binning, the Rowe, NM site is utilizing more of the available spectral information than I am in my backyard.

What's striking to me about this latest comparison is the fact that my aperture is larger by 2x (4x light gathering power), and my pixel size is 10% smaller (1.8 arcsec/pix, vs 2 arcsec/pix), both of which mean that I should be able to sample finer nebular detail a bit better than Rowe, NM with my equipment in my backyard. Yet I still show inferior performance.

There is another way to examine the data. When you tease apart the downsampled astro-images into wavelet layers, it clearly shows that Rowe, NM produces feature elements with higher signal to noise ratio than my own images from my backyard. This is most noticeable at the smaller scale lengths = finer detail. As we approach larger scale lengths that difference begins to diminish and we see large scale structures about equally well, except for background noise limitations. I would expect a 1/F spectral structure in the noise too, so small scale structures will be damaged by sky background noise and poor seeing more than large scale structures.

So... in the back of my mind begs the question: If I were to get the same kind of QSI mono camera, would I see any improvement in my images with regard to small-scale structure? I think the above examination says the answer will be "No".