Conventional Wisdom

Back when the leading imaging technology was CCD, it was very important to match your pixel size to your optical system.  Undersampling meant boxy stars.  Oversampling meant less sky coverage and potentially worse signal-to-noise ratio (SNR), though that could often be mitigated via analog binning.  My favorite formula was:

Pixel size (arc-sec) = 206 * pixel size (microns) / focal length (mm)

For optimal sampling you would aim for a pixel size that would give you 2.5 to 3 pixels across the Full Width Half Maximum (FWHM) of your star images.  This is enough to meet the Nyquist sampling criteria, while maintaining maximum sky coverage and avoiding oversampling.

For example, if your typical seeing was 2.5 arc-seconds FWHM, then a 1 arc-second pixel was ideal.  A 9 micron pixel on a 2000 mm focal length telescope gives you 0.93 arc-seconds – perfect for those conditions.  If you were on a mountaintop with better seeing you could use a smaller pixel or a longer focal length.

I don’t recommend that rule of thumb anymore.  Why not?

The New Generation

The latest generation of high performance active pixel CMOS sensors has changed everything.

Most CMOS sensors have relatively small pixels.  As an example, our popular large format Aluma AC455 and Aluma AC461 cameras, using SONY IMX455 and IMX461 sensors respectively, have a pixel size of just 3.76 microns.  This compares to 9 microns for the venerable KAF-18603 CCD sensor found in our now-retired STX-16803 cameras.

Despite the small pixel size in these two sensors, the overall array size is similar to the KAF-16803.  There’s just a lot more pixels!  While the KAF-16803 had 16 megapixels, the IMX455 has 61 megapixels, and the IMX461 has 102 megapixels.  Area-wise, the IMX455 is slightly smaller than the KAF-16803, and the IMX461 is slightly larger.  So the overall sky coverage is similar at the same focal length.

So isn’t oversampling going to be a disadvantage?  Not anymore.

What really changes the math is the read noise.  Typical CCD sensors had read noise in the 9 to 15 electron range.  This is the noise that is added in to every pixel on every exposure.  These new CMOS sensors, at 1X gain for maximum well depth, have dramatically better read noise of just 3 electrons.  Most users, though, operate at 3X gain because at that gain these sensors produce a spectacular 1.2 electrons per pixel!  That is a massive improvement over CCDs.

Read noise no longer matters.

End of the Conventional Wisdom?

One of the advantages of CCD technology is analog on-chip binning.  This meant you could combine pixels with no added noise.  CMOS sensors by and large don’t do on-chip binning.  The IMX428 can do 1×2 analog on-chip binning; most others can’t even do that.

Back in the day, analog binning was a big winner for noise, because at 2×2 binning you read just once for every four pixels.  When you digitally bin 2×2, you get 2x as much read noise.  (Math: 4 pixels added root-sum-square means total noise is sqrt(4) = 2 times, so the read noise is therefore 2X that of an unbinned pixel.)  When you bin 3×3 you get 3X the read noise.  This would be a lot of noise for a CCD, but the read noise of the best modern active pixel CMOS is incredibly low.

Let’s compare:

• KAF-16803 CCD sensor:  12 e- read noise.  Digital bin 2×2 = 24 e-, but analog bin is always 12 e-.
• IMX455 CMOS sensor at 1X gain:  3 e-.  Digital bin 2×2 = 6 e-. Digital bin 3×3 = 9 e-.
• IMX455 CMOS sensor at 3X gain:  1.2 e-.  Digital bin 2×2 = 2.4 e-.  Digital bin 3×3 = 3.6 e-.

The CMOS sensor wins in every scenario.  We have one customer who needs to bin 512 pixels to make a measurement… that is the only application where the CCD wins.  For everything else the CMOS sensor wins hands-down.

These new sensors are so quiet that, in most imaging situations, the sky background shot noise is larger than the read noise.  Since noise adds root-sum-square you won’t even see the effect of the smaller noise source.  Sky background dominates SNR.

Read noise no longer matters, really!

Why Oversampling is Good

With the new sensors, there are several reasons why you might want to oversample:

• Exceeding optimal Nyquist sampling no longer matters from a noise perspective.
• If the chip is physically large enough to cover the illuminated circle of your telescope’s focal plane (or simply cover enough sky to meet your needs), then it doesn’t matter if the pixels are small.
• In post-processing, extra resolution allows you to perform steps such as align-and-stack without losing resolution.
• You actually get more dynamic range:  if a bright star is spread out over multiple pixels, it takes far longer to saturate.
• If you 2×2 software bin during processing you get 18 bits of data despite getting 1 bit more noise – you actually gain 1 bit of dynamic range compared to binning in the camera.

That’s right – with these new sensors if you have too much sampling, it’s still better to take images at full resolution!  You can always down-sample during image processing if needed.  In fact, the only reason to acquire images with binning is if you’re running out of disk space – and these days disk space is very cheap.