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Message: <blockquote data-quote="typo" data-source="post: 3175327" data-attributes="member: 83808">Ron,Sorry to be so slow to reply. I've been a bit busy and I needed to do a lot of checking and managed to confuse myself several times with the mathematics.Lets recap. The first of the Monarch experiments in #57. The MTF5 was 14.3 cycles/degree. That is 3600/14.3 or 251 arcseconds. Divide that by the 8x magnification and that is 31.5 arcseconds which is the formula you gave in #50. Edmunds give a nice simple definition of the Nyquist limit (though there may be others).<a href="http://www.edmundoptics.co.uk/technical-resources-center/imaging/resolution/" target="_blank">http://www.edmundoptics.co.uk/technical-resources-center/imaging/resolution/</a>“The highest frequency which can be resolved by a sensor, the Nyquist frequency, is effectively two pixels or one line pair.”  In the #57 experiment the Nyquist limit is around 16 cycles/degree. Am I right in thinking anything to the right of the Nyquist limit can be ignored as artefact? So that would be (3600/16)/8 or 28.1”. So 28.1” is the theoretical limit of resolution for the sensor derived from the system parameters you entered for the system and 31.5 is the actual observed limit for the whole system. Is that right so far?I pretty much agree with your calculation for the maximum resolution for the camera in #69 though I had to follow the Imatest formula to get there.<a href="http://www.imatest.com/docs/sharpness/" target="_blank">http://www.imatest.com/docs/sharpness/</a>I calculated 182 cycles/degree or about 20” for two pixels and 10” for one. So that gives a theoretical maximum resolution of 20/8 or about 2.5” (Nyquist Limit) but if we take the experimental value of 2.8 pixels per cycle that becomes 3.5”. A nine fold difference from the fitted MTF of 31.5”. 2.5” or 3.5 "sounds like it's cutting it fine for full aperture testing doesn't it?So we have a dilemma that your experimental results give a resolution value of 31.5” but the system potentially could resolve 3.5”. Did you use a different focal length for the experiment? The Camera has a range from about 8.9 to 71.2mm or an 8 fold range. Using the Imatest formula for cycles/degree  (Pi/180) x (cycles/mm) x (focal length mm). The short axis of the sensor is 6.6mm and a 1920 short axis gives a theoretical 145 cycles/mm. The camera has a potential 22.5 cycles/degree at widest angle or 26.7 arcseconds for the system resolution. If we use the correction of the experimental 2.8 pixels/cycle compared to the 2 pixels/cycle Nyquist limit of 1.4x that would be 31.5”, which is the value we first calculated.I'd suggest that the two results for the Monarch 8x36 were camera limited and the most the most likely explanation is that the images were taken at the shortest focal length. I've found nothing that would suggest a resolution for the Monarch of 7”. Have I got anything wrong?David</blockquote>

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