![]() It also had a number of processes up and running that I don't recognize. None of these files included the pdf of the book. Even so, it proceeded to install some 1,300 files in 400 folders before the installer failed (which likely was because of its being sandboxed). Then it tried to install a number of other programs and change my default browser-nine separate items across three pages (I dismissed all of these). Next, it asked me to accept the terms of an ad-supported download program (within the sandbox, I did so). The first thing it did was try to get administrator privileges (within the sandbox, I complied). I was curious to see what that Website's executable would do, so I ran it in a "sandbox" (a virtual environment where suspect software can be safely tested without making actual changes to your computer). I transcribed here from my hardcover copy. A good search function is "Modulation Transfer Function". 0070592543 and use their Look Inside function. The book I referenced is accessible in bits and pieces through Amazon. If it's not, let me know and I'll try to dig it out some other way. I'm hoping the answer to your question is in there somewhere. (NA > 1 can be achieved only when you're working in dense media with refractive index > 1, and then I think it's actually a little confusing to keep track of what wavelengths and angles the formulas are really talking about.) One way to think about the cutoff frequency is that it scales linearly with NA and reaches its peak value at two cycles per wavelength (one for each lobe of a sine wave) when NA=1. Figure 1.25 at illustrates that the shape of the curve has to do with the aperture shape: a circular aperture gives the form described above while a square aperture gives linear falloff. 50% MTF is reached at about 40% of the cutoff frequency 10% MTF is reached at about 80% of the cutoff frequency. I like to remember the curve as being a little below linear falloff from 0 to the cutoff frequency. That posting also has some other comments about how the numbers vary depending on what assumptions you make and how you define what you're talking about. ![]() The shape of the MTF curve for a perfect optical system (with a round aperture) is shown as the lower curve at. (Look at the f/11 image with a micrometer scale superimposed on it.) Cutoff at f/11 would be 165 cycles/mm, which agrees nicely with the experimental result shown at. So for example with lambda = 0.00055 mm/cycle and NA = 0.125 (f/4), the cutoff frequency would be 454 cycles/mm. Note that the term within parentheses in Eq (4.11), being a cosine, cannot exceed unity this then is the source of Eq. Where nu is the spatial frequency, lambda is the wavelength, and NA = n sin u is the numerical aperture. The modulation transfer factor for a specific frequency is the ratio of the modulation in the image to that in the object, orįor a perfect optical system the modulation transfer function is given byĮquation (4.10): MTF(nu) = 2/pi * (phi - cos(phi)*sin(phi))Įquation (4.11): phi = arccos((lambda*nu)/(2*NA)) Where max and min are, respectively, the maximum and minimum values of brightness (in the object) or illumination (in the image) and the object is a pattern of parallel lines whose brightness varies according to a sine function. The modulation transfer function (MTF) describes the way that the optical system transfers contrast or modulation from object to image, as a function of spatial frequency. ![]() It is an absolute cutoff, with zero contrast between the light and dark lines in the image. This frequency corresponds to a line spacing equal to the Sparrow criterion in Eq. An optical system is a low-pass filter, in that it cannot transmit information at a spatial frequency higher than the cutoff frequency, given (in cycles per unit length) byĮquation (4.6): nu_0 = (2*NA)/lambda = 1/(lambda*f-number) Line resolution is the ability to separate or recognize the elements of a pattern of alternating high and low brightness parallel lines. ![]()
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