In Goodman’s text Introduction to Fourier Optics, optical Fourier transformation can be achieved via lens. In one of the methods the object is placed in front of the lens and the object is close to the lens. If the aperture of lens is infinite, the prefect Fourier transformation can be achieved in the focal plane. Here, we ignore the phase. However, if the aperture of lens is finite, we get the convolution, in which the prefect Fourier transformation is convoluting with the point spread function.
That did raise the question. According to the convoluting expression, the high quality of Fourier transformation is achieved when the aperture of lens is big. However, if the aperture of lens is bigger than the object, it seems that the rest of lens has no effects on optical Fourier transformation. Does the rest of lens has effects on Fourier transformation?
What is the accurate description of this transformation when the object is close to the lens?
Hi Yaokun,
Did you think why LENS could perform Fourier transform?
In my point of view, it is under the paraxial approximation.
Suppose we have a device that could do FT rigorously, the larger the device aperture, the better the FT results. It is because larger aperture coule deal with more spatial spectrum of the object. Of course, diffraction from the object to the device should be considered.
May it help.
Wenhui Zhang
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