Extinction meters tended to provide inconsistent results because they depended on subjective interpretation and the light sensitivity of the human eye, which can vary from person to person.[7]

In a typical scene, many elements are not flat and are at various orientations to the camera, so that for practical photography, a hemispherical receptor usually has proven more effective for determining exposure. Using values of 12.5 for K {\displaystyle K} and 330 for C {\displaystyle C} gives

White light interferometrypdf

With a hemispherical receptor, ISO 2720:1974 recommends a range for C {\displaystyle C} of 320 to 540 with illuminance in lux; in practice, values typically are between 320 (Minolta) and 340 (Sekonic). The relative responses of flat and hemispherical receptors depend upon the number and type of light sources; when each receptor is pointed at a small light source, a hemispherical receptor with C {\displaystyle C} = 330 will indicate an exposure approximately 0.40 step greater than that indicated by a flat receptor with C {\displaystyle C} = 250. With a slightly revised definition of illuminance, measurements with a hemispherical receptor indicate "effective scene illuminance."

With a K {\displaystyle K} of 14, the reflectance would be 17.6%, close to that of a standard 18% neutral test card. In theory, an incident-light measurement should agree with a reflected-light measurement of a test card of suitable reflectance that is perpendicular to the direction to the meter. However, a test card seldom is a uniform diffuser, so incident- and reflected-light measurements might differ slightly.

Another way to avoid under- or over-exposure for subjects with unusual reflectance is to use a spot meter: a specialized reflected-light meter that measures light in a very tight cone, typically with a one degree circular angle of view. An experienced photographer can take multiple readings over the shadows, midrange, and highlights of the scene to determine optimal exposure, using systems like the Zone System.

Amongst other factors the separation of the fringes depends on the wavelength of the light. The shape of the fringes depends on the orientation of the mirrors which if exactly at right angles to one another produces circular fringes and if at other angles to one another can produce straight line fringes.

Although a light meter can take the form of a very simple handheld tool with one-button operation, there are also many advanced light-measurement systems available for use in numerous different applications. These can be incorporated into automated systems that can, for example, wipe lamps clean when a certain reduction in output is detected, or that can trigger an alarm when lamp-failure occurs.

White light interferometryapplications

For incident-light meters, camera settings are related to ISO speed and subject illuminance by the incident-light exposure equation:

The reason a white light source is more difficult to use than a monochromatic source is really very simple: visible fringes are easier to obtain when a monochromatic source is used. This is because monochromatic light has a longer coherence length. Fringes are only visible if the difference in path lengths is less than the coherence length. So, if the coherence length is just a few microns as in the case of white light, the two path lengths must be adjusted to be equal within a few microns - which is not always easy. An LED typically has a coherence length of 12 microns or so; and a diode laser can have a coherence length of meters. It's very easy to obtain fringes immediately after setting up a Michaelson interferometer with a laser source, but can be very tedious to obtain fringes with a white light source.

At best, a flat card is an approximation to a three-dimensional scene, and measurement of a test card may lead to underexposure unless adjustment is made. The instructions for a Kodak neutral test card recommend that the indicated exposure be increased by 1⁄2 step for a frontlighted scene in sunlight. The instructions also recommend that the test card be held vertically and faced in a direction midway between the Sun and the camera; similar directions are also given in the Kodak Professional Photoguide. The combination of exposure increase and the card orientation gives recommended exposures that are reasonably close to those given by an incident-light meter with a hemispherical receptor when metering with an off-axis light source.

In practice, additional complications may arise. Many neutral test cards are far from perfectly diffuse reflectors, and specular reflections can cause increased reflected-light meter readings that, if followed, would result in underexposure. It is possible that the neutral test card instructions include a correction for specular reflections.

Many modern consumer still and video cameras include a built-in meter that measures a scene-wide light level and are able to make an approximate measure of appropriate exposure based on that. Photographers working with controlled lighting and cinematographers use handheld light meters to precisely measure the light falling on various parts of their subjects and use suitable lighting to produce the desired exposure levels.

The earliest calibration standards were developed for use with wide-angle averaging reflected-light meters (Jones and Condit 1941). Although wide-angle average metering has largely given way to other metering sensitivity patterns (e.g., spot, center-weighted, and multi-segment), the values for K {\displaystyle K} determined for wide-angle averaging meters have remained.

But in order to get interference, wasn't the point to get the light beams to follow different optical paths? This all just seems slightly contradictory to me.

For determining practical photographic exposure, a hemispherical receptor has proven more effective. Don Norwood, inventor of incident-light exposure meter with a hemispherical receptor, thought that a sphere was a reasonable representation of a photographic subject. According to his patent (Norwood 1938), the objective was

One advantage of using a white light source is that it can be used to set up the interferometer with equal path length to within a fraction of a wavelength as only then will a zero order white fringe will be visible.

In most cases, an incident-light meter will cause a medium tone to be recorded as a medium tone, and a reflected-light meter will cause whatever is metered to be recorded as a medium tone. What constitutes a "medium tone" depends on meter calibration and several other factors, including film processing or digital image conversion.

A uniform perfect diffuser (one following Lambert's cosine law) of luminance L {\displaystyle L} emits a flux density of π {\displaystyle \pi } L {\displaystyle L} ; reflectance then is

to provide an exposure meter which is substantially uniformly responsive to light incident upon the photographic subject from practically all directions which would result in the reflection of light to the camera or other photographic register.

When the word light meter or photometer is used in place of radiometer or optometer, or it is often assumed the system was configured to see only visible light. Visible light sensors are often called illuminance or photometric sensors because they have been filtered to be sensitive only to 400-700 nanometers (nm) mimicking the human eyes' sensitivity to light. How accurately the meter measures often depends on how well the filtration matches the human eyes' response.

White light interferometrymicroscope

Reflected-light meters measure the light reflected by the scene to be photographed. All in-camera meters are reflected-light meters. Reflected-light meters are calibrated to show the appropriate exposure for "average" scenes. An unusual scene with a preponderance of light colors or specular highlights would have a higher reflectance; a reflected-light meter taking a reading would incorrectly compensate for the difference in reflectance and lead to underexposure. Badly underexposed sunset photos are common exactly because of this effect: the brightness of the setting sun fools the camera's light meter and, unless the in-camera logic or the photographer take care to compensate, the picture will be grossly underexposed and dull.

With a slightly revised definition of reflectance, this result can be taken as indicating that the average scene reflectance is approximately 12%. A typical scene includes shaded areas as well as areas that receive direct illumination, and a wide-angle averaging reflected-light meter responds to these differences in illumination as well as differing reflectances of various scene elements. Average scene reflectance then would be

The problem with trying to measure a wavelength of the light which makes up white light is that as soon as a mirror is moved only a little from a position when the light path lengths are equal the white light fringe disappears, coloured fringes replace it and then as the mirror moves further the fringes disappear.

It is commonly stated that reflected-light meters are calibrated to an 18% reflectance,[10] but the calibration has nothing to do with reflectance, as should be evident from the exposure formulas. However, some notion of reflectance is implied by a comparison of incident- and reflected-light meter calibration.

ISO 2720:1974 calls for reflected-light calibration to be measured by aiming the receptor at a transilluminated diffuse surface, and for incident-light calibration to be measured by aiming the receptor at a point source in a darkened room. For a perfectly diffusing test card and perfectly diffusing flat receptor, the comparison between a reflected-light measurement and an incident-light measurement is valid for any position of the light source. However, the response of a hemispherical receptor to an off-axis light source is approximately that of a cardioid rather than a cosine, so the 12% "reflectance" determined for an incident-light meter with a hemispherical receptor is valid only when the light source is on the receptor axis.

White light contains a continuous range of wavelengths each of which produce an interference pattern with a different fringe separation. It is only when the path lengths of the two beams which form the interference pattern are equal that constructive interference occurs at the same region for all wavelengths and that is often called the zero order fringe and is shown below in the middle of the diagram.

However, it is said that one of the disadvantages of this interferometer is that it doesn't allow for accurate measures when the light source is white light, but I don't really understand why that's the case.

The constants K {\displaystyle K} and C {\displaystyle C} shall be chosen by statistical analysis of the results of a large number of tests carried out to determine the acceptability to a large number of observers, of a number of photographs, for which the exposure was known, obtained under various conditions of subject manner and over a range of luminances.

The sensor will send a signal to the meter that is proportional to the amount of light that reaches the sensor after being collected by the optics and passing through the filter. The meter then converts the incoming signal (typically current or voltage) from the sensor into a reading of calibrated units such as Foot-Candles (fc) or Lux (lm/m^2). Calibration in fc or lux, is the second most important feature of a light meter. It not only converts the signal from V or mA, but it also provides accuracy and unit to unit repeatability. National Institute of Standards and Technology (NIST) traceability and ISO/IEC 17025 accreditation are two well known terms that verify the system includes a valid calibration.

Range: for systems that are not linear and auto ranging this function allows the user to select the portion of the meter electronics that best handles the signal level in use.

White light is broadband and larger the bandwidth, lesser the coherence time. The last represent the time in which there is a fixed phase relationship. Since interference depends upon phases, it's important to have a fixed phase relationship.

White lightinterferometer thickness measurement

In Scientific Research & Development uses, a light meter consists of a radiometer (the electronics/readout), a photo-diode or sensor (generates an output when exposed to electromagnetic radiation/light) a filter (used to modify the incoming light so only the desired portion of incoming radiation reaches the sensor) and a cosine correcting input optic (assures the sensor can see the light coming in from all directions accurately).

As one moves away from the centre you could have a bright fringe due to one wavelength occurring at a position where there is a dark fringe of another wavelength. Thus moving out from the centre the fringe patterns due to each of the wavelengths which make up white light overlap so much that no further fringes are discernable. With while light one might see a central white fringe and a few coloured fringes and then a uniform illumination.

After a quick search on Wikipedia, they essentially say that the difference in the optical paths followed by the two light-beams needs to be inferior to the coherence length of the light source to produce significant interference contrast, so since white light has a low coherence length (of the order of $10^{-6}$m), the optical paths need to be practically the same for both light beams.

The incident-light calibration constant depends on the type of light receptor. Two receptor types are common: flat (cosine-responding) and hemispherical (cardioid-responding). With a flat receptor, ISO 2720:1974 recommends a range for C {\displaystyle C} of 240 to 400 with illuminance in lux; a value of 250 is commonly used. A flat receptor typically is used for measurement of lighting ratios, for measurement of illuminance, and occasionally, for determining exposure for a flat subject.

A light meter (or illuminometer) is a device used to measure the amount of light. In photography, an exposure meter is a light meter coupled to either a digital or analog calculator which displays the correct shutter speed and f-number for optimum exposure, given a certain lighting situation and film speed. Similarly, exposure meters are also used in the fields of cinematography and scenic design, in order to determine the optimum light level for a scene.

White light interferometryresolution

Interference pattern has a visibility, meaning how better can the fringes distinguished. The visibility is related to the degree of first order coherence $g^{(1)}$, a measure of amplitude-amplitude correlation. It indicates the fact that exist a fixed relationship between the phases at different instant of time, or different position along the beam.

Calibration of cameras with internal meters is covered by ISO 2721:1982; nonetheless, many manufacturers specify (though seldom state) exposure calibration in terms of K {\displaystyle K} , and many calibration instruments (e.g., Kyoritsu-Arrowin multi-function camera testers[11] ) use the specified K {\displaystyle K} to set the test parameters.

In a Michelson Interferometer, a light beam is split into 2 different beams that travel different optical paths, through the "arms" of the interferometer. Then, they are reflected and, finally, recombined to form a single light beam again. But because they traveled optical paths of different lengths these beams will have a phase diference between them, which will result in an interference pattern. The straight-forward method makes the device easy to build and use.

Yes, the difference in path length is indeed what is measured in an interferometer, but if fringes can only be seen when the path length is less than the coherence length, white light only allows a very small range of path length difference to be measured: a few microns. With a coherence length of meters, a laser can be used in an interferometer to measure path length changes that vary from a fraction of a micron to several meters, all with sub-micron precision.

Along with having a variety of features, a light meter may also be usable for a variety of applications. These may include the measurement of other bands of light such UVA, UVB, UVC and Near IR. For example, UVA and UVB light meters are used for phototherapy or treatment of skin conditions, germicidal radiometers are used for measuring the UVC level from lamps used for disinfection and sterilization, luminance meters are used to measure the brightness of a sign, display or exit sign, PAR quantum sensors are used to measure how much of a given light source's emission will help plants grow, and UV-curing radiometers test how much of the lights emission is effective for hardening a glue, plastic, or protective coating.

For reflected-light meters, camera settings are related to ISO speed and subject luminance by the reflected-light exposure equation:

White light InterferometryZYGO

Light meters also are used in the general field of architectural lighting design to verify proper installation and performance of a building lighting system, and in assessing the light levels for growing plants.

Light meters or light detectors are also used in illumination. Their purpose is to measure the illumination level in the interior and to switch off or reduce the output level of luminaires. This can greatly reduce the energy burden of the building by significantly increasing the efficiency of its lighting system. It is therefore recommended to use light meters in lighting systems, especially in rooms where one cannot expect users to pay attention to manually switching off the lights. Examples include hallways, stairs, and big halls.

Later[when?] meters removed the human element and relied on technologies incorporating selenium, CdS, and silicon photodetectors.

There are other types of specialized photographic light meters. Flash meters are used in flash photography to verify correct exposure. Color meters are used where high fidelity in color reproduction is required. Densitometers are used in photographic reproduction.

Coherence length is defined: $l_c = c\tau_c$, where c is the speed of light. When the fringe pattern is computed there is an oscillatory term that depends on the path lengths difference and a prefactor that is the modulus of the first order coherence. Taking for example chaotic light with collision broadening you have an exponential decay of the degree of first order coherence, like $\exp(-\frac{\tau}{\tau_c}) $. If you take the lengths path difference $|z_1 - z_2|$ much smaller than the coherence length $l_c$, this term can be high and so the visibility, since $\tau = \frac{|z_1 - z_2|}{c}$. Extremely small coherence time $\tau_c$ implies necessarily to take impractical extremely small paths difference.

To measure wavelength using the interferometer changes one of the path lengths by moving a mirror a measured distance and counting the fringes which cross a graticule in the field of view and each complete fringe movement corresponding to the mirror being moved half a wavelength of the light. To get a reasonable estimate of wavelength one might measure the distance the mirror moves when $50$ fringes traversed the field of view.

Meter calibration establishes the relationship between subject lighting and recommended camera settings. The calibration of photographic light meters is covered by ISO 2720:1974.

The next exposure meters, developed at about the same time but not displacing actinometers in popularity until the 1920s and 1930s, are known as extinction meters, evaluating the correct exposure settings by variable attenuation.[4] One type of extinction meter contained a numbered or lettered row of neutral density filters of increasing density. The photographer would position the meter in front of their subject and note the filter with the greatest density that still allowed incident light to pass through. In another example, sold as Heyde's Aktino-Photometer starting from the early 1900s, the photographer views the scene through an eyepiece and turns the meter to vary the effective density until the scene can no longer be seen.[6] The letter or number corresponding to the filter strength causing the "extinction" of the scene was used as an index into a chart of appropriate aperture and shutter speed combinations for a given film speed.[3]: 72

Many modern cameras include sophisticated multi-segment metering systems that measure the luminance of different parts of the scene to determine the optimal exposure. When using a film whose spectral sensitivity is not a good match to that of the light meter, for example orthochromatic black-and-white or infrared film, the meter may require special filters and re-calibration to match the sensitivity of the film.

Illuminance is measured with a flat receptor. It is straightforward to compare an incident-light measurement using a flat receptor with a reflected-light measurement of a uniformly illuminated flat surface of constant reflectance. Using values of 12.5 for K {\displaystyle K} and 250 for C {\displaystyle C} gives

The earliest exposure meters were called actinometers (not to be confused with the scientific instrument with the same name), first developed in the late 1800s after commercial photographic plates became available with consistent sensitivity. These photographic actinometers used light-sensitive paper; the photographer would measure the time required for the paper to darken to a control value, providing an input to a mechanical calculation of shutter speed and aperture for a given plate number.[3]: 69  They were popular between approximately 1890 and 1920.[4]

White lightinterferometer working principle

There are, however, significant obstacles to overcome in order to achieve a successful implementation of light meters in lighting systems, of which user acceptance is by far the most formidable. Unexpected or too frequent switching and too bright or too dark rooms are very annoying and disturbing for users of the rooms. Therefore, different switching algorithms have been developed:

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In practice, the variation of the calibration constants among manufacturers is considerably less than this statement might imply, and values have changed little since the early 1970s.

What you see beyond the zero fringe is the fringes pattern of different wavelengths overlapping one another. So for the first bright fringe beyond the centre (first order fringe) it is blue (short wavelength) on the "inside" and violet" (longer wavelength) on the outside because the blue light has the smallest fringe separation and the violet light the largest fringe separation.

Some light meters also have the ability to provide a readout in many different units. Lux and footcandles are the common units for visible light, but so are Candelas, Lumens, and Candela per square meter. In the realm of disinfection, UVC is typically measured in watts per square centimeter, or watts for a given individual lamp assembly, whereas systems used in the context of the curing of coatings often provide readouts in Joules per Square centimeter. Regular measurements of UVC light intensity thus can serve to provide assurance of proper disinfection of water and food-preparation surfaces, or reliable coating hardness in painted products.

White light interferometryvs confocal

This pitfall (but not in the setting-sun case) is avoided by incident-light meters which measure the amount of light falling on the subject using a diffuser with a flat or (more commonly) hemispherical field of view placed on top of the light sensor. Because the incident-light reading is independent of the subject's reflectance, it is less likely to lead to incorrect exposures for subjects with unusual average reflectance. Taking an incident-light reading requires placing the meter at the subject's position and pointing it in the general direction of the camera, something not always achievable in practice, e.g., in landscape photography where the subject distance approaches infinity.

Selenium and silicon light meters use sensors that are photovoltaic: they generate a voltage proportional to light exposure. Selenium sensors generate enough voltage for direct connection to a meter; they need no battery to operate and this made them very convenient in completely mechanical cameras. Selenium sensors however cannot measure low light accurately (ordinary lightbulbs can take them close to their limits) and are altogether unable to measure very low light, such as candlelight, moonlight, starlight etc. Silicon sensors need an amplification circuit and require a power source such as batteries to operate. CdS light meters use a photoresistor sensor whose electrical resistance changes proportionately to light exposure. These also require a battery to operate. Most modern light meters use silicon or CdS sensors. They indicate the exposure either with a needle galvanometer or on an LCD screen.

Exposure meters generally are sorted into reflected-light or incident-light types, depending on the method used to measure the scene.

Units: For illuminance the units are typically only lux and foot-candles but many light meters can also be used for UV, VIS and IR applications so the readout could change to W/cm^2, candela, Watts etc.

If a scene differs considerably from a statistically average scene, a wide-angle averaging reflected-light measurement may not indicate the correct exposure. To simulate an average scene, a substitute measurement sometimes is made of a neutral test card, or gray card.

One source produces two light beams which appear to come from two "coherent" (virtual) sources which traverse two paths and then superpose to produce an interference pattern consisting regions of different intensities - light and dark fringes.

ISO 2720:1974 recommends a range for K {\displaystyle K} of 10.6 to 13.4 with luminance in cd/m2. Two values for K {\displaystyle K} are in common use: 12.5 (Canon, Nikon, and Sekonic[8]) and 14 (Minolta,[9] Kenko,[9] and Pentax); the difference between the two values is approximately 1⁄6 EV.