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Measurement of Energy/Light - Source Measurements, Surface Measurements, Radiometers, Spectroradiometers, Light Meters

detector material scene incident

Radiometry and photometry include two broad categories of measurement: (1) measures of energy/light emitted (or reflected) from point or extended area sources, and (2) measures of energy/light falling onto surfaces. While fundamental physical differences exist between the two cases, it is important to note that many of the characteristics of both measures are common and that the surface upon which the energy/light falls reflects some fraction of the energy/light and may be considered an extended source itself.

Electromagnetic radiation is carried in traveling waves made up by electric and magnetic fields that vary periodically in time and position. The spectrum of EM radiation spans 20 orders of magnitude, from gamma rays to electric power transmissions. Electromagnetic radiation can be described by it wavelength (l), the distance over which the wave completes one full cycle. Electromagnetic radiation can also be described by its frequency, the number of cycles the wave undergoes per unit time. The common unit of measure for frequency is the Hertz (Hz), the number of cycles per second. The frequency is equal to the reciprocal of the period, where the period is the length of time it takes for the wave to go through one complete cycle. Since all EM radiation travels through a vacuum at 3 × 10 8 m/s, its wavelength (measured in meters) and frequency (measured in cycles per second) are related by

c = ? · v

where c is the speed of EM radiation in a vacuum, ? is the wavelength, and n is the frequency.

The human eye is not sensitive to the majority of the energy in the EM spectrum. The sensitivity is restricted to a very narrow range of wavelengths nominally spanning the range from 400 to 700 nm. In addition to this restricted range, the visual system is not uniformly sensitive within this region. The CIE V (?) function describes the average relative sensitivity from 350 to 750 nm under daylight conditions. The peak response for the human visual system in daylight is approximately 555 nm or 5.4 × 10 14 Hz.

Source Measurements

The simplest case of radiometric or photometric source measurement involves a theoretical point source of radiant energy, defined as an infinitely small source, emitting energy equally in all directions. This theoretical point source does not exist, but small sources observed at a large distance serve as a reasonable approximation. Usually, if the viewing distance is ten times greater than the source’s greatest dimension, this approximation holds true.

As was mentioned previously, radiant or luminous intensity is the measure of energy into a solid angle in any given direction. The intensity of the source is invariant with distance from the source. The intensity is, however, variant with direction due to the non-uniform-emitting behavior of real-world, non-theoretical point sources. For example, the filament of a tungsten lamp enclosed in a clear bulb will exhibit more intensity when viewed from its side than it does when viewed down its length. Intensity does not serve as a very useful quantity for many applications because of this variance in magnitude due to direction and the fact that implied in its definition is an ever-increasing surface area on an encompassing sphere onto which the energy falls. To have a constant measurement of intensity, the detector would need to grow proportionately to this increase in projected surface area.

For these reasons, irradiance or illuminance are typically better measures for most imaging or photographic applications. Remember that irradiance or illuminance is a measure of energy per unit area falling onto a surface (watts or lumens per square meter). The irradiance or illuminance emitting from a point source is inversely proportional to the square of the distance between the source and the detector used to measure it. For instance, if the intensity emanating in a particular direction is measured using a 1 cm 2 detector at a distance of 1m away from a source, the area of the detector can be thought of as the area on the surface of a sphere through which the energy propagating is measured. If the distance at which this intensity was measured was now doubled, that is 2m away, the surface area through which the energy would now propagate for the same solid angle would be 4 times as large (since the surface area of a sphere is 4p 2 ). Now if the same detector is placed at this new distance, it would only capture 1/4 of the photons in this solid angle, and therefore the irradiance or illuminance at this point in space would be 1/4 the value it was at a distance of 1 m.

This phenomenon is known as the inverse square law; namely that the illuminance or irradiance produced by a point source is inversely proportional to the square of the distance from the source. In radiometric terms, this is represented by where I is the radiant intensity emitted by the source and r is the distance (or radius of a sphere surrounding the source) at which the energy in measured.

In addition to irradiance and illuminance falling off with distance from a source, the measured irradiance or illuminance will fall off with angle from the normal to the surface onto which the energy is incident. As a surface is tilted with respect to the direction of the incoming energy, the projected area onto that surface increases in proportion to the cosine of the tilt angle. As such, the energy measured by a detector that is parallel to the surface will fall off with this same proportionality since the effective area that it presents to the source gets smaller (e.g., hold a coin by its edges between your fingers and slowly tilt it so that the normal to its face points away from your eye—the area that you see gets smaller). In radiometric terms

E ? = E 0 cos(?)

where E 0 is the irradiance measured with a detector perpendicular to the incident energy, E ? ; is the irradiance measured by the tilted detector, and ? is the angle at which the detector is tilted.

Surface Measurements

Energy reflected from a surface serves as a secondary source with measurable radiance. These surfaces serve as extended sources. The radiant output from an extended source is described in terms of the rate at which energy is emitted into a solid angle in a given direction per unit area of the source, or its radiance as we referred to this earlier.

The radiance of an extended source is invariant with viewing distance. Because the surface of the extended source can be thought of as an infinite collection of point sources, the loss of energy from each point due to viewing distance is exactly made up for by the increase in the surface visible within a given solid angle as the distance increases.

The radiance in a particular direction reflected from a surface is proportional to the irradiance falling onto the surface at a particular angle to the source. In radiometric terms, this is given by

Measurement Devices

There are many different devices used to measure energy or light. These devices vary in design as well as in the sensitive material that they use to detect the amount of incident energy. Whether we are talking about radiometry or photometry, the design of these instruments is the same, the difference between radiometers and photometers is that the detector of a photometer is spectrally filtered by the CIE V (?) function mentioned earlier. This will become apparent later in the discussion of spectroradiometers.

Radiometers

Instruments that measure any of the radiometric quantities mentioned previously are called radiometers. Radiometers must rely upon detectors that are sensitive to the energy range of interest. There are at least two common classes of radiometers in use today.

The first class measures radiant power indirectly by monitoring the secondary effect to a material’s physical properties of the incident EM radiation. An example of this type is the bolometer. Incident energy causes thermal variation within the detector material. This thermal variation causes the electrical resistance of the material to change. The radiometric incident energy is therefore calculated by comparing the resistance to the resistance of the material in the absence of any incident radiation.

A second class of radiometers is based on photoelectric detectors. These detectors are made of materials whose electronic characteristics change as a function of incident radiant power. There are several different types of photodetectors used in radiometers. Photoemissive detector materials release electrons when struck by radiant energy. Photomultiplier tubes are one example of a photoemissive detector. Photovoltaic detector materials are semi-conductor devices in which incident energy creates a potential difference across a boundary layer, converting incident energy to an electrical voltage. Selenium cells are an example of a photovoltaic detector. Photo conductive detector materials change the conductance in proportion to the amount of incoming radiant energy. Cadmium sulfide cells are an example of this type of detector material.

The detector materials mentioned above, as well as other materials used for detectors, vary in the way they react to incident radiation not only due to the magnitude, but also due to the wavelength of the incident radiant energy. For instance, a selenium cell may produce a greater potential difference (voltage) when exposed to 50 lumens per square meter of radiation at 550 nm than it does to an equivalent illuminance at 450 nm. A plot of the relative response of a detector material to the amount of incoming monochromatic radiant energy is known as a spectral response function for that material. If a constant response from a detector for a constant amount of incident energy at every wavelength were required, then correction factors would need to be computed for each wavelength.

Spectroradiometers

It is quite often desirable to describe the radiant energy emitted by a source or reflected from a surface as a function of wavelength rather than as a single quantity. There are many methods to achieve this goal, some of which are illumination of the material with a monochrometer, dispersion of the energy with a prism or grating, or through the use of interferometers and Fourier mathematics. The common thread among all these techniques is that in the end, the response from the detector material for the amount of incident energy at each wavelength is known. It must be noted that this response is a factor of several different factors: (1) the spectral distribution of energy for the source used, (2) the spectral distribution of the material off of which the energy is reflected (if this is the case), and (3) the relative spectral response of the detector material itself. So the spectral radiant energy at any wavelength may be represented as

F(?) = F S (?)? T (?)ß D (?)

where F s (?) is the radiant energy from the source incident on the target material, ? r (?) is the spectral reflectance of the material, and ß d (?) is the spectral response function for the detector used.

Light Meters

There are two different types of light metering techniques commonly used by photographers—reflective and incident. For meters that use these techniques, there are many different designs and approaches.

Reflective light meters measure the light reflecting off of a subject or the luminance. Designs can include center-weighted metering, spot metering, or matrix metering.

Center-weighted metering looks at the luminance reaching the meter from a large percentage of the scene observed. Typically the angular field of view of these meters is on the order of 25° (a 35 mm format camera equipped with a standard 50 mm lens has a horizontal field of view of 40° and an angular field of view of 46°—very close to the field of view of good visual acuity for the standard human observer). This type of design is typically found in older, non-computerized cameras and also in many hand-held light meters.

Spot metering looks at a very small portion of the scene photographed. The typical field of view for spot meters is 1 to 5°. This design can be modally found in many modern cameras as well as in a host of hand-held meters. The use of a spot meter allows the photographer to determine the luminance for a particular object within the scene photographed to properly determine exposure for that area or to make multiple measurements within the scene to measure the amount of contrast between various scene elements. This latter technique allows the photographer to assign appropriate zone values to scene elements when using the Zone System for exposure determination.

Matrix metering is found in many modern, computer-driven cameras with through the lens (TTL) metering built in. The scene is broken up into as few as 3 or as many as 50 different segments, each of which is metered. These data are then delivered to an algorithm that determines exposure based upon assumptions made about typical scene content. For example, the algorithm might guess that the upper right and left corners of a scene are bright sky, the lower left and right corners are darker ground, and the center is composed of the main subject. With these assumptions made, the individual narrow field of view measurements made at each location are combined in a weighted fashion to arrive at the proper exposure. This will only prove appropriate if the actual scene content and composition meet the assumptions made. More advanced matrix metering systems will track the photographer’s eye within the viewfinder and place the heaviest weighting on the segment, or group of segments, that is co-aligned with the photographer’s gaze.

Metering with a reflective light meter is very intuitive but can prove to be very problematic. For example, if one was at the zoo photographing a polar bear and a black bear under identical illumination conditions, then it is clear that the exposures given to both scenes should be the same. However, if a reflective metering design is used to determine the exposure, one will likely underexpose the scene containing the polar bear while overexposing the scene with the black bear. The reason is that a measurement of the luminance coming from a scene dominated by a highly reflective object, such as the white fur of the polar bear, will be greater than the luminance from the scene dominated by the darkly colored fur of the black bear. The former case will cause the photographer to choose a shorter exposure time or smaller aperture setting than the latter. The reality is that an exposure somewhere between these two would be most appropriate for both.

Reflective light meters used for photographic purposes are almost always designed to compute photographic exposure based on the speed of the film used and the shutter speed or aperture setting that is desired. The proper shutter speed or aperture setting is determined to allow an object that exhibits an average reflectance of 12 to 18 percent across the spectral range of the detector material to produce a density value or digital count in the middle of the dynamic range of the film or digital camera’s detector. With this knowledge, the photographer can choose to accept the suggested exposure or to, in an educated fashion, over- or underexpose the scene to move this exposure point up or down, respectively, to obtain the contrast that is desired.

Incident light meters measure the light or illuminance falling onto a scene. This is typically accomplished using a small white dome, referred to as a cosine receptor or integrating hemisphere, positioned over the detector. This dome is positioned in front of the subject photographed and pointed toward the camera. The dome collects energy falling onto the subject from all directions. This is the illuminance that will be reflected from the subject toward the camera. Again, these meters are most often designed to determine exposure parameters for a particular film speed. The exposure determined will cause a scene element whose reflectance is somewhere between 12 and 18 percent to fall in the middle of the density or digital count dynamic range.

Many modern digital cameras have the ability to produce a digital count histogram for an image that is captured. Digital count histograms represent the number of pixels in the image that have a particular digital count or brightness value. This turns out to be a very useful tool for the photographer and may in time make the use of a light meter less common. The photographer can collect several images of a scene with different exposure settings or illumination setups. Once the images are collected, the histogram can be looked at to determine if a significant number of pixels are collected at either the lower or upper end of the digital count scale. If they are concentrated at the lower extreme, then the image was underexposed and the shutter speed should be decreased or the aperture opened up, whichever is more appropriate. If the opposite is true and a significant number of pixels are collected at the upper end of the digital count range, the image was overexposed and the shutter speed should be increased or the aperture stopped down. While this may not make the “traditional” photographer happy, it is a very viable technique that is becoming more prevalent in its usage.

The detector materials used for both types of meters mentioned above vary, but there are some common ones that are used in the majority of light meters in production today or that you may have in your equipment collection. Each of these materials has benefits and detriments. Some of the more common detector materials used in photographic light/ exposure meters are selenium cells, cadmium sulfide, silicon photodiodes (or silicon blue cells), and gallium arsenide phosphide cells.

Selenium cells were used almost exclusively in meters and cameras prior to the 1970s. Selenium produces a small electrical current when exposed to light, the amount of current proportional to the amount of incident energy. The spectral response function of selenium is comparable to that of typical black and white films. It made for a wonderful detector material that needed no batteries to operate, since it produced its own electrical current. It also functions very well in cold weather when other systems that rely on battery power may begin to fail. This photovoltaic material was great in so many ways except that over time, with exposure to light and moisture, it began to physically deteriorate (a bad quality for a material used in a light meter). Protective measures were used with these meters such as protective caps and the use of desic-cant when storing the meter for prolonged periods of time. These measures extended the life of the detector material, but in time they all failed. Oversensitivity to ultraviolet radiation tended to make meters based on this type of detector material produce artificially high response levels that tended to produce underexposure. In addition, the linearity of the detector material tended to fall off at higher brightness levels, producing less current than might be expected, which resulted in overexposure of the photograph.

Cadmium sulfide is still in use in light/exposure meters today, although it is not as prevalent as it had been in the previous two decades. As part of the photoconductive series of detector materials, the resistance of this material changes as a function of incident energy. As more light falls onto this material, the resistance decreases, thus allowing more current to flow through a circuit containing this component. This material works very well in low light situations, a weakness of the previously mentioned selenium-based meters. Although this meter is not overly sensitive to ultraviolet energy, it does have an enhanced sensitivity to red light and infrared energy. Many systems use a filter to compensate for this enhanced sensitivity, but others do not, so care needs to be taken to understand the characteristics of your meter. If the system is not filtered, underexposure may result for scenes that contain a significant amount of red subject matter or for those that are collected under sources with significant infrared energy, like tungsten lamps.

The main drawback of cadmium sulfide stems from its “memory.” The resistance of the material is slow to increase after exposure to a high luminance scene element. This is typically noticed as a sluggish response from the meter’s output display. One must be sure to give the meter enough time to react when subsequently pointed at a low luminance element, which can sometimes be several minutes in the case of a very bright initial reading.

Silicon photocells (or photodiodes) are the most common detector material used today. These are a semi-conductor material that produces a small electric current due to the promotion of electrons to higher energy states or bands in the material when exposed to incident photons. Although these are photovoltaic in nature, a battery is typically used to drive an amplifying circuit to boost the sensitivity or response of the material. In addition, as is the case for all photovoltaic materials, silicon photocells respond to changes in illuminance levels more than three orders of magnitude faster than the photoconductive materials, such as cadmium sulfide, so there is no significant memory for this material. Meters based on this material also suffer with an enhanced sensitivity to the red end of the spectrum, as was the case with cadmium sulfide; so particular attention needs to be paid to the filtering that is employed in the meter’s design.

Gallium arsenide phosphide cells are photovoltaics and similar in all aspects to silicon photocells except that there is no oversensitivity to energy at the red and longer wavelength regions of the spectrum. This material is more costly to manufacture and is therefore only available in a few cameras in production today.

As with anything in life, there are always trade-offs. It is important that you know the characteristics and behavior of the detector material used in your light or exposure meter and compensate for it either quantitatively by adjusting for the material’s spectral response function, or qualitatively by, for example, knowing you need to open up one stop when your scene contains a lot of red subject matter.

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