The autocorrelation of the square is a triangle-shaped function,įigure 1.25 Universal curves for diffraction-limited MTFs, for incoherent systems with circular or rectangular aperture.Īs an example of the calculations, let us consider the square-aperture system of Fig. As an example of this calculation, we take the simple case of a square aperture, seen in Fig. The diffraction MTF is thus the magnitude of the (complex) diffraction OTF. (1.24) do not exactly undo each other-the diffraction OTF is the two-dimensional autocorrelation of diffracting aperture p( x,y). We then calculate the diffraction OTF in the usual way, as the Fourier transform of the impulse response h( x, y):īecause of the absolute-value-squared operation, the two transform operations of Eq. (1.23), we must implement a change of variables ξ = x/λ f and η = y/λ f to express the impulse response (which is a Fourier transform of the pupil function) in terms of image-plane spatial position. The magnitude squared of the diffracted electric-field amplitude E in V/cm gives the irradiance profile of the impulse response in W/cm 2:įrom Eq. For the incoherent systems we consider, the impulse response h( x,y) is the square of the two-dimensional Fourier transform of the diffracting aperture p( x,y). (1.6), (1.7), and (1.10), which state that the OTF is the Fourier transform of the impulse response. We will show that this is consistent with the definition of Eqs. The diffraction OTF can be calculated as the normalized autocorrelation of the exit pupil of the system.
The diffraction effects are only calculated once per system and do not accumulate multiplicatively on an element-by-element basis. The diffraction MTF is based on the overall limiting aperture of the system (the aperture stop). Aberrations increase the spot size and thus contribute to a poorer MTF. The MTF diffraction is the upper limit to the system’s performance the effects of optical aberrations are assumed to be negligible. Diffraction MTF is a wave-optics calculation for which the only variables (for a given aperture shape) are the aperture diameter D, wavelength λ, and focal length f.