This section describes how to calculate the Point Spread Function (PSF) of an image sensor array. The PSF is a measure of spatial cross talk. In other words, if one pixel is fully illuminated, how much light is detected in the neighboring pixels.
The following figure shows experimental setup being simulated. One pixel of the image sensor is illuminated. We measure the amount of power detected by the neighboring pixels.
Typically the Point Spread Function is defined as the response of the system to a illumination by a point source at a large distance from the camera. In a digital camera, however, the concept of a Point Spread Function must be extended to account for both the spread due to the finite Numerical Aperture (NA) of the lens system, and the spread due to crosstalk in the digital image sensor pixels.
Suppose we take a picture of a flat wall that is painted black, except for one green square. The size of this green square is such that it corresponds to exactly one pixel of the image sensor. (For example, if the wall is 1x1m and the image sensor has 1000x1000 pixels, then the size of the green square should be 1x1mm.) Incoherent, unpolarized light from the green square will propagate away from the wall. Any light within the NA of the lens system will be collected and focused onto the image sensor plane. Ideally, the light will fully illuminate one pixel of the image sensor, without any illumination of neighboring pixels. In practice, the finite NA of the lens system will cause the incoming beam to spread and illuminate more than one pixel, as shown in the following figure. In addition, as the light travels through the image sensor lenses, oxide layers and metallic interconnects some light is scattered into adjacent pixels. Finally, there can be some electrical crosstalk between pixels after the photons have been converted into electron-hole pairs. As a result of all of these effects, an electrical signal will be registered in several pixels rather than a single pixel.
We define the digital Point Spread Function (PSF) as the fraction of power detected in the active region of each pixel as a function of pixel position for the illumination conditions that would ideally result in a response in a single pixel.
Since FDTD is a coherent simulation tool, it is not possible to directly simulate the above system. The problem is that we can't directly reproduce incoherent illumination from the macroscopic lens system. Instead, we recognize that this illumination is equivalent to the sum of a number of incoherent point sources, as shown below.
It is possible to simulate this equivalent system with FDTD. Two simulation are required for each point source position. When the set of simulations are compete, it is possible to reconstruct the desired illumination (incoherent, un-polarized illumination of one pixel).
Note: Thin lens source
The Thin lens option of the Gaussian beam source is perfectly suited these simulations. Simply specify the NA and focal point of your lens system.
See the following pages for 2D and 3D examples. We recommend starting with the 2D example because the simulations run much faster. It is best to gain some basic understanding of the device from fast 2D simulations before starting the more accurate but slower 3D simulations. This is always a good tip, but it is especially true for PSF calculations because of the large number of simulations that are required. Also, the simulation region must be quite large to include several periods of the device.
We can also calculate the modulation transfer function (MTF) by fourier transforming the PSF.