
Agreed. I see such test charts as a convenient way to find where aliasing occurs, without uncertainties due to lens performance, focus accuracy, sensor and demosaic implementations. Arguably of ...

I think the fundamental issue is how far you treat the analysis as a model of continuous analogue quantities one could (in principle) measure in the real world, and where we have a list of numbers ...

Not if the function you are sampling (the light falling on the pixels) varies rapidly with position between sampling points.

No, although if the signal varies smoothly, and has no high frequency modulation any difference is small. If the signal does vary rapidly within a pixel width, then the "sample first" approach ...

I still hold with convolution with the pixel width (or area) first. This low pass filters the input intensity before sampling, as happens in reality. In your scheme, how do you model the case of a ...

If you want to avoid all these concerns over lens choice, micro focus angst, and searching for a subject with appropriate spectral content, you could use a test image like the one I found on Keith ...

Jack, I contend that you have the sampling and convolution in the wrong order. Each pixel integrates the light incident on its surface before sampling. This is particularly important if the source ...

Jack, Hopkins provides an explicit formula (27) for geometric defocus MTF in the absence of both diffraction and higher order aberrations. It has the same form as the field (not intensity) in the ...

I am with Jim in that filtering is best done before downsampling or decimation. I would argue that sampling does not generate new frequencies, but it does shift high spatial frequency spectral ...

In the geometric optics limit with no aberrations, all rays pass through the paraxial focus. In the presence of (positive) spherical aberration, rays emerging near the centre of the lens pass ...

Is this pure defocus, or a combination of defocus and spherical aberration. Is the 0.41 lambda path difference RMS or peakpeak? I don't have the Hopkins paper, but Google tells me it is widely ...

Yes, but why is the lens MTF more or less symmetrical about 157 cycles/mm? I would expect either a monotonically decreasing MTF, or a few ripples imposed on a decreasing trend. I would not expect ...

I still have reservations about what your "above Nyquist" frequency components represent. In figure (1) why does the lens PSF peak at 315 cycles/mm with unit MTF in an analogue/continuous ...

The Fourier transform of the noise in a 2D image is a 2dimensional distribution, which we can plot as a function of horizontal and vertical spatial frequencies, fx, fy. Suppose the noise is ...

Jim was referring to SNR which is a ratio, so necessarily after normalisation by the signal  or were you thinking of a reduction of N oise to S ignal R atio (which I often find myself doing). Not ...

Yes  ringing at close to Nyquist frequency, though the amplitude shouldn't be very large.

OK, Nyquist in the original is 102 cycles/mm. OK, the dashed lines (labelled 2:1 downsampling), are (apart from the 0.5 scaling) representative of the original image before downsampling. I would ...

I would argue that it doesn't (or shouldn't without some careful thought and explanation) An MTF is a transfer function. It describes the ratio between contrast in the subject and contrast in the ...

This I don't follow. Why does the contrast drop to half for low spatial frequencies? I don't buy the "stretching" in the Fourier domain. This may be related to bobn2's comments about frequency ...

I was ignoring all the DFT steps, simply thinking about what MFT means. Forget for a moment that the data comes from a slanted edge. Imagine that you have photographed a series of sinusoidally ...
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