Rogers G L
Appl Opt. 1979 Sep 15;18(18):3152-5. doi: 10.1364/AO.18.003152.
A number of authors have pointed out that a system of zone plates combined with a diffuse source, transparent input, lens, and focusing screen will display on the output screen the Fourier transform of the input. Strictly speaking, the transform normally displayed is the cosine transform, and the bipolar output is superimposed on a dc gray level to give a positive-only intensity variation. By phase-shifting one zone plate the sine transform is obtained. Temporal modulation is possible. It is also possible to redesign the system to accept a diffusely reflecting input at the cost of introducing a phase gradient in the output. Results are given of the sine and cosine transforms of a small circular aperture. As expected, the sine transform is a uniform gray. Both transforms show unwanted artifacts beyond 0.1 rad off-axis. An analysis shows this is due to unwanted circularly symmetrical moire patterns between the zone plates.
许多作者指出，由波带片系统与漫射源、透明输入物、透镜及聚焦屏组合而成的系统，将在输出屏上显示输入物的傅里叶变换。严格来讲，通常显示的变换是余弦变换，双极性输出叠加在直流灰度级上，以给出仅为正值的强度变化。通过对一个波带片进行相移可得到正弦变换。时间调制是可行的。以在输出中引入相位梯度为代价，重新设计该系统以接受漫反射输入也是可行的。给出了一个小圆形孔径的正弦和余弦变换结果。正如所料，正弦变换是均匀灰度。两种变换在离轴0.1弧度之外都显示出不需要的伪像。分析表明，这是由于波带片之间不需要的圆形对称莫尔条纹造成的。
