tag:blogger.com,1999:blog-6555460465813582847.post2038969312105770156..comments2023-02-07T10:24:13.796+02:00Comments on MTF Mapper: Pixels, AA filters, Box filters and MTFfvdberghhttp://www.blogger.com/profile/06566624298120266140noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-6555460465813582847.post-75500651095884350212017-09-05T10:00:32.170+02:002017-09-05T10:00:32.170+02:00Hi Frans,
thank you very much - especially for yo...Hi Frans,<br /><br />thank you very much - especially for your very fast answer. <br />In the meantime, I gave it a thought once again and did find an explanation for my questions. I'm glad, my thought goes with your statement. :)<br />But with the pi-factor - I didn't know. I will look especially into this, to scale my axis. (I'm writing on my masters thesis)<br /><br />So, thank you once again & have good time,<br />Thorsten<br />privatehttps://www.blogger.com/profile/13902623229977139676noreply@blogger.comtag:blogger.com,1999:blog-6555460465813582847.post-9152758075215998732017-08-30T10:24:48.533+02:002017-08-30T10:24:48.533+02:00Typo: second last paragraph "function will sp...Typo: second last paragraph "function will span from -2.5 micron to 5 micron" should be "unction will span from -2.5 micron to 2.5 micron"fvdberghhttps://www.blogger.com/profile/06566624298120266140noreply@blogger.comtag:blogger.com,1999:blog-6555460465813582847.post-356050634865889352017-08-30T10:21:31.931+02:002017-08-30T10:21:31.931+02:00Hi Thorsten,
I can clarify the scale of the axes ...Hi Thorsten,<br /><br />I can clarify the scale of the axes a bit. If we stick to pixel units, then things are relatively simple: our box filter is exactly 1 unit (pixel) wide. We can model this as the unit rectangular function (https://en.wikipedia.org/wiki/Rectangular_function), i.e., the box starts at -0.5 pixels, and ends at 0.5 pixels. <br /><br />This box function is the Point Spread Function (PSF) of our system (which consists of only the sensor). The MTF of our system is the magnitude of the Fourier Transform of the PSF.<br /><br />As the Wikipedia page tells us, the Fourier transform of rect(x) is sinc(f), where sinc(f) is defined as sin(pi*f)/(pi*f). Since the sinc(f) function is real (not complex), we can compute the magnitude of the Fourier transform (=MTF) of our PSF simply as the absolute value of the result, i.e., our MTF is |sinc(f)|, or |sin(pi*f)/(pi*f)|.<br /><br />What scale do we use for "f"? Well, since our box function PSF was defined in units of pixels, we naturally obtain units of 1/(pixel) for "f", or as I prefer, "cycles per pixel". Strictly speaking I should say "cycles per pixel pitch". <br /><br />Anyhow, note the "pi*" factor in the definition of the sinc(f) function! This is what causes the first zero of |sinc(f)| to fall at f=1.0.<br /><br />If we want to convert to physical units, we simply have to scale both the x-axis in the PSF domain, and the f-axis in the MTF domain. For example, if our photosite pitch is 5 micron, then our box function will span from -2.5 micron to 5 micron (just multiply x-axis values by 5 micron). In the frequency (MTF) domain, we multiply the f-axis values by 200 to obtain a line-pairs-per-mm frequency scale. The factor 200 is simply 1000/5, i.e, 1/(5 micron) but expressed in mm.<br /><br />And finally, yes, the MTF plots are all one-sided power (magnitude) spectrum plots. This appears to be a convention when talking about MTF.<br /><br />-F<br /><br /><br />fvdberghhttps://www.blogger.com/profile/06566624298120266140noreply@blogger.comtag:blogger.com,1999:blog-6555460465813582847.post-17102662626207798892017-08-30T09:52:01.097+02:002017-08-30T09:52:01.097+02:00Yes, of course you plotted the one sided power spe...Yes, of course you plotted the one sided power spectrumprivatehttps://www.blogger.com/profile/13902623229977139676noreply@blogger.comtag:blogger.com,1999:blog-6555460465813582847.post-56476760643690931552017-08-30T09:39:01.993+02:002017-08-30T09:39:01.993+02:00Hey there,
I'm reading your article to underst...Hey there,<br />I'm reading your article to understand the MTF of one Pixel and how this affects the overall MTF of an imaging system.<br />But for me, it is not clear, how your box shaped filter merges into the sinc-function. How did you scale your x-axis?<br />For my understanding, you have to squeeze the pixel width/pixel pitch into the fourier-transform/sinc-function to get the first location of MTF = 0.<br />Also, did you plot the one sided power amplitude spectrum (magnitude)?<br /><br />I would appreciate if you could answer this for me! :) Either here or via eMail (zwinger@hm.edu)<br /><br />Best Wishes,<br />Thorstenprivatehttps://www.blogger.com/profile/13902623229977139676noreply@blogger.comtag:blogger.com,1999:blog-6555460465813582847.post-79090690788607015212012-05-28T15:10:56.141+02:002012-05-28T15:10:56.141+02:00Maybe someone from Nikon is reading this. Let us h...Maybe someone from Nikon is reading this. Let us hope they agree :)fvdberghhttps://www.blogger.com/profile/06566624298120266140noreply@blogger.comtag:blogger.com,1999:blog-6555460465813582847.post-54666555787536559912012-05-28T11:53:08.943+02:002012-05-28T11:53:08.943+02:00Time to get a Nikon D800E. Your work requires it ;...Time to get a Nikon D800E. Your work requires it ;-)<br />Thanks for posting!Anonymoushttps://www.blogger.com/profile/15567515150153861579noreply@blogger.comtag:blogger.com,1999:blog-6555460465813582847.post-30331169750103813532012-05-28T09:51:17.597+02:002012-05-28T09:51:17.597+02:00Thanks!
I would imagine that cross-talk could intr...Thanks!<br />I would imagine that cross-talk could introduce some low-pass filtering effects. Unfortunately, I do not have such a sensor to test --- all my cameras that can provide raw data have OLPFs.fvdberghhttps://www.blogger.com/profile/06566624298120266140noreply@blogger.comtag:blogger.com,1999:blog-6555460465813582847.post-81178598620825162542012-05-28T09:23:10.235+02:002012-05-28T09:23:10.235+02:00Very insightful and well explained, as usual! I am...Very insightful and well explained, as usual! I am just wondering about the 'perfect' box filter assumption for the sensor pixels. Are there no electronic (ex. readout, cross-talk) effects that induce a non-boxfilter PSF?Riaan van den Doolhttps://www.blogger.com/profile/05717170044864295391noreply@blogger.com