Is the original analysis correct? Would CMY yield lower SNR in RGB?
Full link with excerpts below.
http://www.astrosurf.com/buil/us/cmy/cmy.htm"No dominant abnormal color affect the tricolor images of figures 3 and 4. Moreover, the balance of the colors of these two images is extremely similar what is the sign that the calibration procedure starting from a Solar-analog star is working properly. The trichromatic image resulting from data CMY appears slightly denser, but the choice of the thresholds of visualization plays a role here. For better apprehending the difference between these images it is a good idea to try an analysis of the signal to noise ratio in the two situations.
We will simplify by considering that the noise is primarily dominated by the signal itself, i.e. that the reading noise of the CCD is negligible. That does not changes basically the results and in any case, it is this photon noise regime which dominates in the analyzed images which were obtained in suburban environment ( the sky background having a level very high).
First of all, let's analyze the case of a tricolor image resulting from RGB filters. For a given pixel one can consider that the signal S is the sum of the 3 tricolor components:
S = R + G + B
In photon noise dominant situation, the noise N is:
The signal to noise ratio is thus equal to:
Let us see now the case of a trichromatic image synthesized starting from CMY filters. Is R', G' and B' the RGB channels calculated starting from the images taken through CMY filters (CMY2RGB command). According to the equations set (1) we have:
R' = Y + M - C
G' = Y + C - M
B' = C + M - Y
and:
S = R' + G' + B' = Y + M - C + Y + C - M + C + M - Y = C + M + Y
The noise associated with calculation of each channels R', G' and B' is equal to the quadratic sum of the noises of the images C, M and Y (the evaluation of the signal for a channel utilizing two additions and one subtraction and note that the signal is uncorrelated for the different images). This noise is identical for the three channels and is equal to:
The production of the tricolor image requires the three channels R', G' and B', so the final noise is then:
N = SQR(3) . N' = SQR(3 . (C + M + Y))
The signal to noise ratio is thus equal to:
By noting that in theory one must have:
C = G + B
M = R + B
Y = R + G
the preceding equation becomes:
The coefficient 2 which appears in this equation traduct the fact announced to the beginning of this paper that imagery CMY makes it possible to acquire twice more signal in spectral bands RGB than can provide directly a filter set RGB.
While comparing with the value of the signal to noise ratio in the case of the use of filters CMY it appears that subtractive technique RGB brings a profit of:
In other words, for identical exposure time, use of RGB filters increases signal to noise ratio of 22% compared to use of CMY filters. One supposes here that these two sets of filters produce equivalent losses by absorptions and reflexions and that R=G=B and C=M=Y at the output of the CCD camera. This simplified analysis shows that the use of CMY filters does not authorize to decrease the exposure times by a factor two compared to traditional filters RGB and there is no gain to use CMY filters in this situation! "
It should be still underlined that filters CMY can be at the origin of a loss of resolution because of the presence of the atmospheric phenomenon of refraction (it is easier to correct the effect with RGB images obtained directly). Also, obtain images correctly calibrated for a scientific application (calculation of the color equations) is very problematic from CMY images.
In conclusion, the use of CMY subtractive filter in the place of RGB filter is a valid option to carry out realistic color images of astronomical objects. It is noted that the first configuration allows a benefit in signal to noise ratio only for very faint objets and in my peculiar case of transmission filter (these is dispersion in the transmission curve of different sets filters). However this gain is not high in this peculiar situation. The reason comes from the contribution of noise because of the arithmetic operations between images to extract RGB components starting from the observations carried out through CMY filters. In the example shown here it appears that the chromatic balance is more homogeneous with filters RGB than with CMY filters (that indicates that it would be necessary to integrate signal longer through filters cyan and yellow compared to the magenta filter). The problem involved in the recovery of the spectral lines in the case of RGB imagery is not necessary real. Lastly, whatever the technique is used, it is very simple to calculate the calibration coefficients to be applied to the images starting from a star similar to the Sun to obtain images having a pleasant visual aspect having a colors balance close to the visual apparence that a human eye would perceived it (but remember reserve for scientific use of the CMY data...).
