Abstract

We investigate the synthesis of binary images through diffraction-limited cameras employing high-contrast detection. This involves finding an input image, which when passed through the bandlimited camera and clipped by the detector gives a desired binary image. The problem is equivalent to finding a bandlimited 2-D function with prescribed zero-crossings. In the 1-D case, one can always find a bandlimited function of finite energy whose zero-crossings within an interval of finite extent are prescribed. This implies that a form of superresolution is possible within an interval of finite extent. The method is based on modifying the zeros of sinc(2Bx) (B being the bandwidth) by inserting the prescribed zeros to replace an equal number of zeros. We have extended this method to a 2-D function f(x,y) by dividing it into 1-D slices, g_k(x) ⁼ f(x,y_k). Each slice is synthesized to have the correct zero-crossings up to an arbitrary scaling factor a_k. An orthogonal slice, say h(y) = f(x₀,y), is synthesized to have the correct zero-crossings. The scaling factors are then determined by matching the amplitudes of orthogonal slices, h(y_k) = a_kg_k(X₀). With sufficiently close slices, the synthesized 2-D function can satisfy all requirements.

© 1986 Optical Society of America