Doug Kerr
Well-known member
We rarely hear about the frequency response (MTF, if you will) of the antialising filters in typical cameras with CFA sensors.
The type of filter that is usually used takes an incoming "point" of light in the image and splits it into four points (in two stages - first it doubles it in one direction and then in the other).
In a classical design used with a CFA array, the spacing (both horizontally and vertically) between the pairs of points is half the distance between the sensels of the color group (for the R or B groups). (That is actually one times the "developed image pixel pitch".)
If we take this "point spread function" and take its Fourier transform, we will get the frequency response of this filter. Interestingly enough, that turns out to be (the absolute value of) a cosine function, starting at 1 for zero frequency and declining with increasing frequency until it reaches zero at the Nyquist frequency of the color group. (That is half the Nyquist frequency of the entire image.)
With regard to averting aliasing in the color group, that's not as good as a"brick wall" response, but is pretty appropriate (and has the advantage that we can actually make it).
Now, the response rises again as the frequency further increases (the cosine function itself goes negative after reaching zero). This is not desirable, but it is overcome by other considerations, including the "aperture effect" of the sensel acceptance area not being infinitesimal (another kind of lowpass filter function that is in the loop).
But note that its cutoff frequency is at half the Nyquist frequency of the final image pixel array. This is the basis of the outlook that the antialising filter is harmful to our lust for image sharpness consistent with the pixel pitch of the final developed image.
Wheeler and Rodriguez, in their paper on the tradeoff between protection against chromatic aliasing and degradation of image "sharpness", report that, in a study on which all "imperfections" in an image were considered in a single "score", an antialising filter of this type but with a spot spacing of 0.9 times the color group sensel pitch (not 0.5) - that is, whose "cutoff" frequency is 1.8 times the Nyquist frequency of the color group, or 0.9 times the Nyquist frequency for the entire "developed" image - produced the highest overall score (of course based on certain assumed values of various other system parameters).
Best regards,
Doug
The type of filter that is usually used takes an incoming "point" of light in the image and splits it into four points (in two stages - first it doubles it in one direction and then in the other).
In a classical design used with a CFA array, the spacing (both horizontally and vertically) between the pairs of points is half the distance between the sensels of the color group (for the R or B groups). (That is actually one times the "developed image pixel pitch".)
If we take this "point spread function" and take its Fourier transform, we will get the frequency response of this filter. Interestingly enough, that turns out to be (the absolute value of) a cosine function, starting at 1 for zero frequency and declining with increasing frequency until it reaches zero at the Nyquist frequency of the color group. (That is half the Nyquist frequency of the entire image.)
With regard to averting aliasing in the color group, that's not as good as a"brick wall" response, but is pretty appropriate (and has the advantage that we can actually make it).
Now, the response rises again as the frequency further increases (the cosine function itself goes negative after reaching zero). This is not desirable, but it is overcome by other considerations, including the "aperture effect" of the sensel acceptance area not being infinitesimal (another kind of lowpass filter function that is in the loop).
But note that its cutoff frequency is at half the Nyquist frequency of the final image pixel array. This is the basis of the outlook that the antialising filter is harmful to our lust for image sharpness consistent with the pixel pitch of the final developed image.
Wheeler and Rodriguez, in their paper on the tradeoff between protection against chromatic aliasing and degradation of image "sharpness", report that, in a study on which all "imperfections" in an image were considered in a single "score", an antialising filter of this type but with a spot spacing of 0.9 times the color group sensel pitch (not 0.5) - that is, whose "cutoff" frequency is 1.8 times the Nyquist frequency of the color group, or 0.9 times the Nyquist frequency for the entire "developed" image - produced the highest overall score (of course based on certain assumed values of various other system parameters).
Best regards,
Doug