Optical resolution

Each of these contributes (given suitable design, and adequate alignment) to the optical resolution of the system; the environment in which the imaging is done often is a further important factor.

The results below are based on mathematical models of Airy discs, which assumes an adequate level of contrast.

Real optical systems are complex, and practical difficulties often increase the distance between distinguishable point sources.

In confocal laser-scanned microscopes, the full-width half-maximum (FWHM) of the point spread function is often used to avoid the difficulty of measuring the Airy disc.

[1] This, combined with the rastered illumination pattern, results in better resolution, but it is still proportional to the Rayleigh-based formula given above.

Also common in the microscopy literature is a formula for resolution that treats the above-mentioned concerns about contrast differently.

The above estimates of resolution are specific to the case in which two identical very small samples that radiate incoherently in all directions.

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.

For resolution measurement, film manufacturers typically publish a plot of Response (%) vs. Spatial Frequency (cycles per millimeter).

Solid state sensor and camera manufacturers normally publish specifications from which the user may derive a theoretical MTF according to the procedure outlined below.

They also have a decay time, so the pyroelectric system temporal response will be a bandpass, while the other detectors discussed will be a lowpass.

For the picture to appear to have approximately the same horizontal and vertical resolution (see Kell factor), it should be able to display 228 cycles per line, requiring a bandwidth of 4.28 MHz.

If the line (sensor) width is known, this may be converted directly into cycles per millimeter, the unit of spatial resolution.

There are two methods by which to determine "system resolution" (in the sense that omits the eye, or other final reception of the optical information).

The first is to perform a series of two-dimensional convolutions, first with the image and the lens, and then, with that procedure's result and a sensor (and so on through all of the components of the system).

The other method is to transform each of the components of the system into the spatial frequency domain, and then to multiply the 2-D results.

Although this method is considerably more difficult to comprehend conceptually, it becomes easier to use computationally, especially when different design iterations or imaged objects are to be tested.

For example, in a security or air traffic control function, the display and work station must be constructed so that average humans can detect problems and direct corrective measures.

Other examples are when a human is using eyes to carry out a critical task such as flying (piloting by visual reference), driving a vehicle, and so forth.

Typical test charts for Contrast Transfer Function (CTF) consist of repeated bar patterns (see Discussion below).

where When the system can no longer resolve the bars, the black and white areas have the same value, so Contrast = 0.

When using other methods, including the interferogram, sinusoid, and the edge in the ISO 12233 target, it is possible to compute the entire MTF curve.

The first is to determine the quality of a lens system (see LUPI), and the second is to project a pattern onto a sensor (especially photographic film) to measure resolution.

which is the power to which 2 should be raised to obtain the spatial frequency of the first element (e.g., group -2 is 0.25 line pairs per millimeter).

The spatial frequency is printed alongside each triple bar set, so the limiting resolution may be determined by inspection.

The original application called for placing the chart at a distance 26 times the focal length of the imaging lens used.

The gradually expanding lines near the center are marked with periodic indications of the corresponding spatial frequency.

The idea is analogous to the use of a white noise pattern in acoustics to determine system frequency response.

A multiburst signal is an electronic waveform used to test analog transmission, recording, and display systems.