After now almost two years of practical experience in astrophotography—far too short a time for this demanding work —I summarize for myself some fundamental image principles and look back on some of the insights gained. I do this exemplarily on the basis of a current project, the Tadpoles Nebula (IC 410). Let us start from the beginning, with the most important concepts of astrophotography…

Signal & Noise

As – in astrophotography – Signal and Noise are mathematical concepts, the starting point for the concept of Signal is a Gaussian Distribution. The Gaussian distribution describes how random measurement errors are statistically distributed around a mean value. For almost any continuous variable (variables which can take any fractional amount as height, weight, length etc.) the Gaussian Bell Curve is representative for the data, showing a normal distribution.

If wed like to describe countable things (integer values like the number of raindrops etc.) we use discrete distributions for data description. As the brightness of light – according to Einsteins model – arrives in discrete packets (=Photons), we basically count integer values, when we practice astrophotography. The Photons are perceived to be normally distributed discrete variables. The analogon to the Gaussian distribution for continuous variables is the Poisson Distribution for counting integers. The overall shape of the Poisson Distribution is similar to the Gaussian Curve, but – as integers are counted – there are no fractional values between the integers. However, Poisson Distributions have one big advantage: in order to describe them, we only need one figure: the mean μ . This is because the standard deviation σ (the measure of the deviation of values around the mean) is always the square root of the mean.

The concept of Signal & Noise now describes Signal as the mean μ and Noise as its random fluctuation around it, the standard deviation σ. Noise therefore describes the accuracy of our photon count – the lower the noise the more accurate the measurement becomes. In astrophotography we try to increase the Signal with as many measurements we are able to achieve – we increase the exposure time!

But why do longer exposures (more measurements) increase mainly the Signal? What, if Noise is also increased?

In order to provide the answer, it is necessary to understand the source of Noise: basically we encounter two types of Noise, which is shot noise and read noise. The first being time dependant, as these are random fluctuations of the Signal. Read noise are small errors in the electrical process of measuring and is not time-dependant.

Photon Count Example

For visualization purposes we define the „long-term average rate of photon arrival“ as being the Signal / the mean μ . Imagine just one photosite on the sensor and the true (or real) rate of photon-arrival should be μ = 100 photons per minute. We consider the Poisson Distribution, giving that the standard deviation will always be the square root of the mean, therefore σ = √100 = 10. Therefore 68% of all measurements will be in a range of the standard deviation of +/- 10 photons per minute around the mean of μ = 100 (95% within 2 x σ = +/-20 and 99% within 3 x σ = +/-30).

The more photons we count (the longer the exposure time becomes), the higher our mean values will get. A mean of μ = 10.000 photons per minute results in σ = √10.000 = 100. Exactly at this point the answer to our question is obvious: noise grows at a slower rate than the signal! 100 times the Signal means only 10 times the Noise! At a mean of 100 our SNR was 10 (100/10) – at a mean of 10.000 the SNR becomes 100 (10.000/100). In other words: as noise grows only with the square root of the signal we need four times of the exposure time to double the SNR!

At the beginning, these theoretical foundations were somehow abstract to me and did not seem to offer any real practical value. Over time, however, I have come to understand the benefit of this fundamental theoretical framework. I will try to illustrate and clarify it using a practical example.

IC410 in H-alpha

Let’s take a single capture of the actual project IC 410 (the Tadpoles Nebula in Auriga, Link to NGC 1893 and IC410). The following shows a the raw-file of a single 300-second exposure through an H-alpha filter. The capture was screen-stretched with PixInsight`s STF (Screen Transfer Function) in order to make the faint structures visible for inspection without altering the underlying linear pixel values.Using PIs SubFrameSelector Tool, we are able to measure the Signal-to-Noise Ratio (SNR) for this single frame revealing SNR = 3,39.

In order to increase accuracy of our „photon count“ (= astrophotography), I´ve captured 45 H-alpha frames over two imaging nights. In total 3 hours and 45minutes of exposure time was collected. The 45 frames were registered, calibrated and integrated in order to receive the following master file (again screen-stretched with STF). Signal-to-Noise Ratio now is five times higher and increased to SNR = 16,62.

The SNR measured with the SubframeSelector in PixInsight is subject to uncertainties, since it is affected by background gradients, object structure, and seeing conditions. As I understand it, this is only a relative measure for comparing frames rather than as an absolute SNR value!

In the next blog, I will address the topics of sampling and seeing in more detail. For now, however, I would like to present the actual processing of the H-alpha channel, as a kind of appetizer 🙂