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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.

A longpass filter is said to have an “angle of incidence” at which it begins to transmit light. This angle is usually about 30 degrees from the surface of the filter. Above this angle, the filter will appear increasingly transparent. Below this angle, the filter will appear increasingly opaque.

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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.

MTFOptics

As the wavelength of light increases, the transmission curve of a longpass filter begins to level off and eventually becomes flat. This means that longer wavelengths of light are more likely to be transmitted through the filter than shorter wavelengths.

Achromatic lenses are a type of optical device that has a variety of applications in everyday life. This lens is made up of two different types of glass, each with a different level of refraction. When the light passes through the lens, it is combined and results in a clear image. Achromatic lenses can be…

Longpass filters are used to block short wavelength light while allowing longer wavelengths to pass. This makes them useful for a variety of applications, including:

Modulation transfer function

What are longpass filters and what do they do? This is a question that many people have, but don’t know where to find the answer. In this blog post, we will discuss longpass filters and what they are used for. We will also talk about the different types of longpass filters and how they can be used to improve your photography skills.

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.

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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.

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MTF lenstest

If you’re working on an optical system design that needs any of these capabilities, then a longpass filter may be the right choice for you.

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Longpass filters are important for certain applications because they allow for the transmission of light at certain wavelengths while blocking out light at other wavelengths. This can be useful in a number of different settings, such as when trying to view objects that are emitting light at specific wavelengths.

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.

Lens MTFcomparison

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 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.

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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.

Figure 7. A polarizing filter transmits only the component of the wave parallel to its axis, , reducing the intensity of any light not polarized parallel to its ...

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.

MTFcamera

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.

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 Rayleigh criterion stated in the equation θ=1.22λD θ = 1.22 λ D gives the smallest possible angle θ θ between point sources, or the best obtainable ...

Longpass filters can be used to block out unwanted light, such as UV light or blue light. They can also be used to accentuate certain colors in a scene. For example, a yellow longpass filter can be used to make green leaves appear more yellow.

Lens MTFchart

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Lens MTFdatabase

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.

Polarization (also polarisation) is a property of transverse waves which specifies the geometrical orientation of the oscillations. ... In a transverse wave, the ...

A longpass filter is an optical filter that allows light with a wavelength longer than the cutoff wavelength to pass through, while blocking shorter wavelengths. Longpass filters are used in a variety of applications, such as fluorescence microscopy, colorimetry, and machine vision.

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.

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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.

MTFimage quality

There are two main types of longpass filters: absorptive and dichroic. Absorptive longpass filters are made of materials that absorb light at shorter wavelengths, while transmitting longer wavelengths. Dichroic longpass filters are made of thin-film interference coatings that reflect shorter wavelengths and transmit longer wavelengths.

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.

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As their name suggests, longpass filters only allow light with wavelengths above a certain cutoff to pass through. The specific wavelength that is allowed to pass depends on the filter; however, most longpass filters have a cutoff between 450 and 650 nanometers. This means that they will allow red, orange, and yellow light to pass through while blocking blue and violet light.

Longpass filters are available in a variety of cutoff wavelengths, ranging from the visible to the infrared. The specific cutoff wavelength of a longpass filter depends on the material used and the thickness of the film.