Additional explanations of human visual acuity can be found on pages from the Nondestructive testing resource center and Stanford University. Page 3 from Stanford has a plot of the MTF of the human eye. I believe the x-axis units (CPD) are Cycles per Degree, where a pair of 1/60 degree features corresponds to 30 CPD.

Laser cavity modes determine the output characteristics of the laser, such as wavelength, polarization, and spatial distribution of the laser light. The selection of a specific mode of operation is important for many applications, including laser spectroscopy, metrology, and material processing.

Cavity modes inlaser

On the left are two progressive scan images. Center are two interlaced images. Right are two images with line doublers. Top are original resolution, bottom are ...

by SJ Lim · 2015 · Cited by 129 — Complementary metal–oxide–semiconductor (CMOS) colour image sensors are representative examples of light-detection devices.

The sharpness of a photographic imaging system or of a component of the system (lens, film, image sensor, scanner, enlarging lens, etc.) is characterized by a parameter called Modulation Transfer Function (MTF), also known as spatial frequency response. We present a unique visual explanation of MTF and how it relates to image quality. A sample is shown on the right. The top is a target composed of bands of increasing spatial frequency, representing 2 to 200 line pairs per mm (lp/mm) on the image plane. Below you can see the cumulative effects of the lens, film, lens+film, scanner and sharpening algorithm, based on accurate computer models derived from published data. If this interests you, read on. It gets a little technical, but I try hard to keep it readable.

Contrast levels from 100% to 2% are illustrated on the right for a variable frequency sine pattern. Contrast is moderately attenuated for MTF = 50% and severely attenuated for MTF = 10%. The 2% pattern is visible only because viewing conditions are favorable: it is surrounded by neutral gray, it is noiseless (grainless), and the display contrast for CRTs and most LCD displays is relatively high. It could easily become invisible under less favorable conditions.

Most of us are familiar with the frequency of sound, which is perceived as pitch and measured in cycles per second, now called Hertz. Audio components— amplifiers, loudspeakers, etc.— are characterized by frequency response curves. MTF is also a frequency response, except that it involves spatial frequency— cycles (line pairs) per distance (millimeters or inches) instead of time. The mathematics is the same. The plots on these pages have spatial frequencies that increase continuously from left to right. High spatial frequencies correspond to fine image detail. The response of photographic components (film, lenses, scanners, etc.) tends to roll off at high spatial frequencies. These components can be thought of as lowpass filters— filters that pass low frequencies and attenuate high frequencies.

The most common transverse mode is the Gaussian mode, which has a bell-shaped intensity profile and is designated by TEMmn.

Film imaging systems consist of a lens, film, developer, scanner, image editor, and printer (for digital prints) or lens, film, developer, enlarging lens, and paper (for traditional darkroom prints). Digital camera-based imaging systems consist of a lens, digital image sensor, de-mosaicing program, image editor, and printer. Each of these components has a characteristic frequency response; MTF is merely its name in photography. The beauty of working in frequency domain is that the response of the entire system (or group of components) can be calculated by multiplying the responses of each component.

Describelasermodes

Standard Depth of Field (DOF) scales on lenses are based on the assumption, made in the 1930s, that the smallest feature of importance, viewed at 25 cm, is 0.01 inches— 3 times larger. It shouldn't be a surprise that focus isn't terribly sharp at the DOF limits. See the DOF page for more details.

The transverse modes give an indication of the distribution of intensity within the beam cross-section. These modes appear as a pattern of spots and are referred to as transverse electromagnetic, or TEM modes. These modes are created by the width of the laser cavity, which develops a few diagonal modes, and are determined by the shape of the laser beam. A little misalignment of the laser mirrors causes different path lengths for different rays inside the cavity.

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Laser cavity modes depend on the frequency of the laser light, the direction in which it is emitted, and the intensity of the light. The length, shape, and optical properties of the cavity, such as the refractive index of the material within the cavity, also affect the laser cavity modes.

Lasermodes wikipedia

This means that for an 8x10 inch print, the MTF of a 35mm camera (lens + film, etc.) above 55 lp/mm, or the MTF of a digital camera above 2800 LW/PH (Line Widths per Picture Height) measured by Imatest SFR, has no effect on the appearance of the print. That's why the highest spatial frequencies used in manufacturer's MTF charts is typically 40 lp/mm, which provides an excellent indication of a lens's perceived sharpness in an 8x10 inch print enlarged 8x. Of course higher spatial frequencies are of interest for larger prints.

The figure below represents a sine pattern (pure frequencies) with spatial frequencies from 2 to 200 cycles (line pairs) per mm on a 0.5 mm strip of film. The top half of the sine pattern has uniform contrast. The bottom half illustrates the effects of Provia 100F on the MTF. Pattern contrast drops to half at 42 cycles/mm.

Thus, these modes differ in their field distribution along the longitudinal axis. This explains why only specific frequencies are possible inside the cavity. Longitudinal modes appear as a single spot in the laser output. These modes are created by the length of the laser cavity and are determined by the distance between the cavity mirrors and the wavelength of the laser.

Laserlongitudinalmodespacing

The statement that the eye cannot distinguish features smaller than one minute of an arc is, of course, oversimplified. The eye has an MTF response, just like any other optical component. It is illustrated on the right from the Handout #9: Human Visual Perception from Stanford University course EE368B - Image and Video Compression by Professor Bernd Girod. The horizontal axis is angular frequency in cycles per degree (CPD). MTF is shown for pupil sizes from 2 mm (bright lighting; f/8), to 5.8 mm (dim lighting; f/2.8). At 30 CPD, corresponding to a one minute of an arc feature size, MTF drops from 0.4 for the 2 mm pupil to 0.16 for the 5.8 mm pupil. (Now you know your eye's f-stop range. It's similar to compact digital cameras.) Another Stanford page has Matlab computer models of the eye's MTF.

Depth of field refers to the range of distance that appears acceptably sharp. It varies depending on camera type, aperture and focusing distance, although print ...

LaserTEM modes

... mount various AF-Nikkors on the Nikon 1-Series digital cameras. Not all Nikkors are compatible, however. To find out which lens may fit see this list. Mind ...

These standing waves are created when the electromagnetic radiation is forced to move back and forth inside the cavity. In a standing wave, the point at which the amplitude of the waves is at a minimum is called a node, while the point at which the amplitude is at a maximum is called an anti-node. The positive integers m, n, and p give the number of nodes that the standing wave has along the y, z, and x axes, respectively. Each set of values of m, n, and p represents a well-defined cavity mode with a well-defined resonant frequency.

Bi177 – Lecture 8 Contrast vs Resolution vs Detection. Review of Kohler Illumination. Tradeoffs in Contrast/Resolution. Phase Contrast. Dark Field. Rheinberg ...

Laser cavity modes are particular sets of standing wave patterns in a laser cavity. Standing waves, also known as stationary waves, are created when two waves of the same frequency and amplitude but opposite phases interfere with each other. The output of a laser may consist of one mode or a superposition of several modes. These modes that are sustained depend on the boundary conditions, which are determined by the mirrors in a laser cavity, such as the geometry and alignment, as well as the wavelength of the laser.

Transverse modes are standing wave patterns that are perpendicular to the direction of propagation of the laser beam. When the modes have the same p-value but differ in m and n values, the resulting field distributions differ in the transverse direction.

How is MTF related to lines per millimeter resolution? The old resolution measurement— distinguishable lp/mm— corresponds roughly to spatial frequencies where MTF is between 5% and 2% (0.05 to 0.02). This number varies with the observer, most of whom stretch it as far as they can. An MTF of 9% is implied in the definition of the Rayleigh diffraction limit.

Mode-lockedlaser

A laser cavity is an optical resonator in a laser where the lasing action takes place. The cavity is typically made up of two mirrors at each end of the cavity, one of which is partially reflective and allows some of the light to pass through.

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The edges in the bar pattern have been broadened, and there are small peaks on either side of the edges. The shape of the edge is inversely related to the MTF response: the more extended the MTF response, the sharper (or narrower) the edge. The mid-frequency boost of the MTF response is related to the small peaks on either side of the edges.

The number of transverse cavity modes can be controlled by choosing a pinhole diameter equal to the diameter of the lower mode.

Jan 9, 2023 — In the "normal" photodiode, the current is just the generation current, i.e., the current corresponding to the generated charge carriers in the ...

The longitudinal modes are standing wave patterns along the optical axis of the laser. When different modes have the same values for m and n with a unit difference in the p-value, the corresponding difference in frequency of oscillationis:

Lasermodes pdf

The number of longitudinal modes can be controlled by controlling the length of the laser cavity, for example, by reducing the cavity length, and adding an extra mirror inside the cavity.

The light that is trapped inside the cavity between the mirrors is amplified as it bounces back and forth. However, the mirrors at each end lead to the development of both longitudinal and transverse modes superimposed on the beam. The longitudinal modes are standing wave patterns along the optical axis of the laser, whereas the transverse modes are perpendicular to the direction of propagation of the laser beam.

Two-modelaser

At a distance d from the eye (which has a nominal focal length of 16.5 mm), this corresponds to objects of length = (angle in radians)*d = 0.000291*d. For example, for an object viewed at a distance of 25 cm (about 10 inches), the distance you might use for close scrutiny of an 8x10 inch photographic print, this would correspond to 0.0727 mm = 0.0029 inches. Since a line pair corresponds to two lines of this size, the corresponding spatial frequency is 6.88 lp/mm or 175 lp/inch. Assume now that the image was printed from a 35mm frame enlarged 8x. The corresponding spatial frequency on the film would be 55 lp/mm.

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The essential meaning of MTF is rather simple. Suppose you have a pattern consisting of a pure tone (a sine wave). At frequencies where the MTF of an imaging system or a component (film, lens, etc.) is 100%, the pattern is unattenuated— it retains full contrast. At the frequency where MTF is 50%, the contrast half its original value, and so on. MTF is usually normalized to 100% at very low frequencies. But it can go above 100% with interesting results.

The image above represents only 0.5 mm of film, but takes up around 5 inches (13 cm) on my monitor. At this magnification (260x), a full frame 35mm image (24x36mm) would be 240 inches (6.2 meters) high and 360 inches (9.2 meters) wide. A bit excessive, but if you stand back from the screen you'll get an feeling for the effects of the lens, film, scanner (or digital camera), and sharpening on real images.

The red curve is the spatial response of the bar pattern to the film + lens. The blue curve is the combined MTF, i.e., the spatial frequency response of the film + lens, expressed in percentage of low frequency response, indicated on the scale on the left. (It goes over 100% (102).) The thin blue dashed curve is the MTF of the lens only.