Abstract

It is shown that a 2M-point representation I_H(f) of the Hartley intensity spectrum I_Ha(f) can be reconstructed from the intersections of I_Ha(f) with the reference sinusoid R(f) of period 2δ. As required by the Nyquist sampling criterion, one sinusoidal crossing is detected within every frequency interval δ when the bandwidth of I_H (f) is 2Mδ. Specifically, the 2M crossings are used to determine the 2M expansion coefficients [h(mΔ)] of I_H (f) with respect to the Hartley basis functions: cas(2πfmΔ), where Δ = 1/2Mδ and m = −M, −M + 1, . . . ,M. An accurate and efficient algorithm for computing [h(mΔ)] from the sinusoidal crossings also is proposed and demonstrated.

© 1995 Optical Society of America

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