How to know the resulting iso of stacked images?

I've read in several questions like this one that stacking photos helps to reduce the noise of the resulting image, which is really helpful in astrophotography.

My question is if I can know a priori how many photos do I have to take to get an stacked image with X-ISO (Let's say 100). Of which factors does this noise reduction depends on?

It doesn't really work that way. But even if it did, it would depend on the way you stack the images. Do you add them together? Do you average them? Use some other even more complex method?

Stacking multiple images only reduces the influence of photon noise, often called shot noise. Shot noise is caused by the random nature of light. Simplistically put, photons are not evenly distributed in a field of light. Shot noise is random and will change from one frame to the next. Stacking does nothing for read noise. Read noise is caused by the electronics of the sensor and processing pipeline. It remains fairly constant in a series of shots. Most people who stack images also use dark frame subtraction to reduce the influence of read noise.

Noise isn't really caused by using a certain ISO setting. Rather it is caused by the low signal-to-noise ratio that often results from the low light levels that necessitate such high amplification of the signal off the sensor. Unfortunately, amplifying the signal also amplifies the noise.

tl;dr: To get noise levels comparable to one well balanced ISO100 shoot you need 2 ISO200 shots etc. Do not care about that; shoot as many shots as possible and merge them.

Back then, the DIN and ISO values described how much the film reacts (darkens) to the exposure of the light.

ISO values are meant to give simillar results but slightly different way. CCD and CMOS ships gather charge with respect to the ammount of light collected by the pixel. The signal is them processed through A/D converter. If you have 8bit colour depth you have 2^8 dicrete values of the pixel brightness to represent whole scale from black to white.

ISO value is just a factor that is used to multiply the outcoming values to span all values from 0 to 255, in case of 8bit depth.

One factor is the sensor saturation - the maximum charge it can accumulate; or how many photons it can detect.

Second factor is sensor sensitivity - how many photons is needed to raise the reading value by 1 bit; or what charge is generated by one incident photon.

Note that the sensor is not sensitive to visible light only. There is allways some noise - additional random signal with constant amplitude - both on the chip and during the processing. When you are shooting using ISO100 you are using effectively full range of the signal and the signal-to-noise ratio (SNR) is highest. When you switch to ISO200 you multiply the whole signal by 2, you use half of the range with same noise level. Resulting SNR is halved. The higher ISO the narrower range is used and thus SNR is lowered.

Stacking multiple images is used to increase SNR ratio back to acceptable levels. Stacking two images doubles the SNR, because the (desired) signal doubles and noise keep its amplityde (statistically).

If you sum the signals up you increase the imaginary exposure without altering the imaginary ISO.

If you average the signals you reduce the imaginary ISO value without altering the imaginary exposure.

• Exactly how is read noise, which is fairly constant in its location from shot-to-shot, halved by averaging two images? The amount of read noise is doubled just as the amount of signal is before dividing by two. Commented Feb 28, 2017 at 16:27
• Random noise is constant (say 1) in amplitude; from shot-to-shot it adds to every pixel random value between -1 to 1. Sum of random values symetrically distributed around zero converge to zero. Commented Feb 28, 2017 at 19:20
• Random noise is usually referred to as poisson or photon or shot noise. Read noise is not nearly as random and usually follows the same pattern from frame to frame because its source is the electronics and sensor of the camera, not the random nature of light. If the shots are taken in fairly quick succession then the temperature of the sensor and associated electronics is also fairly constant and thus generates roughly the same thermal noise from frame to frame. Commented Feb 28, 2017 at 20:51
• If the read noise varies by +1 to -1 on a scale that can read from 0 to 4095 ( or even 0 to 255) then values that are between +50 and +52 compared to the surrounding pixels are still going to be +51 when averaged. Thermal noise will always be positive. It will never subtract from the signal. Most electrical noise is also positive. Commented Feb 28, 2017 at 20:51