Optical Resolution - Sensor Resolution (spatial)

Sensor Resolution (spatial)

Some optical sensors are designed to detect spatial differences in electromagnetic energy. These include photographic film, solid-state devices (CCD, CMOS detectors, and infrared detectors like PtSi and InSb), tube detectors (vidicon, plumbicon, and photomultiplier tubes used in night-vision devices), scanning detectors (mainly used for IR), pyroelectric detectors, and microbolometer detectors. The ability of such a detector to resolve those differences depends mostly on the size of the detecting elements.

Spatial resolution is typically expressed in line pairs per millimeter (lppmm), lines (of resolution, mostly for analog video), contrast vs. cycles/mm, or MTF (the modulus of OTF)). The MTF may be found by taking the two-dimensional Fourier transform of the spatial sampling function. Smaller pixels result in wider MTF curves and thus better detection of higher frequency energy.

This is analogous to taking the Fourier transform of a signal sampling function; as in that case, the dominant factor is the sampling period, which is analogous to the size of the picture element (pixel).

Other factors include pixel noise, pixel cross-talk, substrate penetration, and fill factor.

A common problem among non-technicians is the use of the number of pixels on the detector to describe the resolution. If all sensors were the same size, this would be acceptable. Since they are not, the use of the number of pixels can be misleading. For example, a 2 megapixel camera of 20 micrometre square pixels will have worse resolution than a 1 megapixel camera with 8 micrometre pixels, all else being equal.

For resolution measurement, film manufacturers typically publish a plot of Response (%) vs. Spatial Frequency (cycles per millimeter). The plot is derived experimentally. Solid state sensor and camera manufacturers normally publish specifications from which the user may derive a theoretical MTF according to the procedure outlined below. A few may also publish MTF curves, while others (especially intensifier manufacturers) will publish the response (%) at the Nyquist frequency, or, alternatively, publish the frequency at which the response is 50%.

To find a theoretical MTF curve for a sensor, it is necessary to know three characteristics of the sensor: the active sensing area, the area comprising the sensing area and the interconnection and support structures ("real estate"), and the total number of those areas (the pixel count). The total pixel count is almost always given. Sometimes the overall sensor dimensions are given, from which the real estate area can be calculated. Whether the real estate area is given or derived, if the active pixel area is not given, it may be derived from the real estate area and the fill factor, where fill factor is the ratio of the active area to the dedicated real estate area.

where

• the active area of the pixel has dimensions a×b
• the pixel real estate has dimensions c×d

In Gaskill's notation, the sensing area is a 2D comb(x, y) function of the distance between pixels (the pitch), convolved with a 2D rect(x, y) function of the active area of the pixel, bounded by a 2D rect(x, y) function of the overall sensor dimension. The Fourier transform of this is a function governed by the distance between pixels, convolved with a function governed by the number of pixels, and multiplied by the function corresponding to the active area. That last function serves as an overall envelope to the MTF function; so long as the number of pixels is much greater than one (1), then the active area size dominates the MTF.

Sampling function:

where the sensor has M×N pixels