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Derivation of the Fourier Transform of the Mask for Optical Heterodyning
 

Summary: Derivation of the Fourier Transform of the Mask
for Optical Heterodyning
Supplement to SIGGRAPH 2007 paper [1]
1 Derivation
This analysis is done for a 1D mask placed in front of a 1D sensor to capture a 2D light
field.
Let v be the total distance between the aperture and the sensor and d be the distance
between the mask and the sensor. Define = d
v . From Figure 1, if we place the 1D
code c(y) at a distance d from the sensor, the resulting 2D light field gets attenuated by
the 2D mask m(x,) given by
m(x,) = c( +(1-)x). (1)
As we will derive below, the Fourier transform of the mask lies on a line in the 2D
Fourier light field space.
Let C(fy) be the 1D Fourier transform of c(y)
C(fy) =

-
c(y)exp(-j2 fyy)dy (2)
and let M(fx, f ) be the 2D Fourier transform of m(x,):

  

Source: Agrawal, Amit - Mitsubishi Electric Research Labs

 

Collections: Engineering