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Photometry, Radiometry, and Measurement - Definitions, Radiometry, Photometry, Color Temperature, Color Temperature Meters

source energy power surface

CARL SALVAGGIO, PH.D.
Rochester Institute of Technology

The terms that we use as practitioners and researchers in a field of study define the discipline itself as well as the effectiveness with which we can communicate among colleagues and others members of our profession. The long-lived fictional character, Humpty Dumpty, from the Lewis Carroll classic Through the Looking Glass , said to Alice “When I use a word, it means just what I choose it to mean, neither more nor less.” Alice replied by saying “The question is, whether you can make words mean so many different things.” The fields of photometry and radiometry have a long history of terminology that is used differently among its participants. Whether in descriptive terms or symbols in equations, this inconsistency often gives rise to confusion and misunderstanding. It is intended that, in this section, the reader will gain an understanding of the concepts that make up these two fields and with that understanding be able to look past the words people use to describe topics and find the meaning in what they are saying.

Radiometry is broadly defined as the measurement and characterization of optical radiation. Optical radiation includes energy with wavelengths in the ultraviolet portion of the electromagnetic (EM) spectra through the long wave infrared region. These wavelengths span the range from 0.01 to 1000 µm (1 × 10 -6 m). Photometry is defined as the measurement of light, the EM energy that the human visual system is sensitive to, weighted by the spectral response function of the eye. These wavelengths, depending on the age and health of the person, span the range from 360 to 830 nm (1 × 10 9 m). As one can see already, the terminology changes when referring to the wavelengths encompassed by these two fields, nanometers for photometry and micrometers for radiometry. Others might refer to the frequency of the energy measured and use units of inverse centimeters (cm -1 ). Look past all the terminology and understand that no matter how one refers to the energy, it remains just that, energy, and exhibits the same properties no matter how one references it.

So as we begin, the difference between radiometry and photometry is primarily that radiometry includes energy over the entire optical spectrum, while photometry has a more limited scope, limited to those wavelengths that humans can see. The terminology used in these two fields is different because of historical influence only. The behavior of energy does not change, just the way it is described.

Definitions

Begin by looking at some of the common terms used in the fields of radiometry and photometry. It is important to understand the concept of area as it is used in these fields as many radiometric and photometric quantities are defined in terms of energy and area.

Projected area is defined as the rectilinear or two-dimensional projection of any volumetric or three-dimensional surface onto a plane normal to the unit vector. The projected area, A projected , is proportional to the original volumetric surface area by a factor equal to the cosine of the angle between the original surface and projected surface normal vectors. This can be noted by where the surface integral of dA represents the original volumetric surface area. For example, the projected area of a circular disc with a radius of 1cm whose surface normal is oriented 30° from the surface normal of the surface that it is projected onto is found as

A projected =cos?(p r 2 ) = cos(30°)p(2) 2 = 10.9 cm 2

This projected area is 1.6cm 2 smaller than the original disc’s area. Why is this important? The amount of energy per unit area that one may measure with a detector may be significantly less than the energy that is actually received from a particular direction in space. How much less? The energy is reduced by the factor shown above, namely cos?. To make an absolute measurement of energy per unit area, one needs to be cognizant of the relative orientation between the incident energy and the detector that is used to make the measurement.

A common but sometimes misunderstood radiometric concept is the solid angle. In plane (two-dimensional) geometry, an angle can be defined as located between two radii of a circle with the vertex at the circle’s center. When the length of the arc cut off on the circumference of the circle by these radii is equal to the radius of the circle, the angle between the two radii is one radian (rad). A solid angle extends this concept to three dimensions. A solid angle is defined in three dimensions as having its vertex in the center of a sphere and with a rectangular projection on the surface of the sphere defined by two plane angles, usually denoted by d ? and d f. When an area on the surface of a sphere is equal to the area of a square whose sides are equal in length to the radius of the sphere, the solid angle is said to be one steradian (sr).

Radiometry

Having these abstract quantities defined, it is now possible to define some of the common terms that are used in radiometry.

Energy (Q) is generally defined as the work that a physical system is capable of doing when changing from its actual state to a specified reference state. In photography, the primary interest lies in the energy carried by photons and the energy released or consumed when electrons transition between energy levels (or bands) in the atomic structure of materials. The unit used to represent energy is usually the Joule (J), which may also be defined as watt-seconds ( W × s ).

Power (F) or radiant flux is the derivative of energy with respect to time, dQ/dt . The unit used is typically the watt (W).

So energy is the integral of power over time. Energy is usually the quantity of choice when referring to an integrating detector (those that build up more signal or contrast with longer exposure) or a pulsed source like a photographic emulsion/charged-coupled device or a mechanically chopped laser. Power is the typical quantity when referencing non-integrating detectors or continuous sources such as a cadmium cell or a tungsten lamp.

We can now look at power with respect to the geometric quantities that were previously presented—area and solid angle.

Irradiance (E) or flux density is a measure of power or radiant flux per unit area on a surface. It is arrived by computing the derivative dF/dA . Irradiance is the amount of illuminating power originating from all directions within a hemisphere falling onto a surface. A similar term with identical units is radiant excitance. Radiant excitance (M) represents the power per unit area leaving a surface into a hemisphere above that surface. The area in the definition of irradiance is that receiving power, while in exitance, it refers to the area emitting power. The units usually used for both these terms are watts per square meter (W/m 2 ).

Radiant exitance can be computed on a per wavelength basis for a blackbody at a known absolute temperature using Planck’s blackbody equation. A blackbody is a hypothetical object that absorbs all incident radiation and is a perfect emitter of radiation because of incandescence. Incandescence is the emission of EM radiation by an object as a result of its temperature. Planck’s blackbody equation is where h is Planck’s constant having a value of 6.6262 · 10 -34 J·s, c is the speed of light with a value of 2.9979 · 10 8 m/s, ? is the wavelength of the energy in units of meters, k is Boltzmann’s constant which is 1.3807 · 10 -23 J/K, and T is the absolute temperature of the blackbody in degrees Kelvin.

Radiant intensity is the time rate of flow of power or radiant flux emitted by a point source in a given direction computed as the derivative of power with respect to solid angle, dF/dO . The units on this quantity are watts per steradian (W/sr). By definition, the intensity of a source is invariant with distance; however, an implied assumption is that the source emits equally in all directions. Virtually no real-world sources demonstrate this behavior. This quantity is strictly defined for point sources, but in application is used for those sources whose dimension is less than 1/10 the distance from which they are observed.

Radiance ( L ) is the power per unit projected area per unit solid angle and is defined as the derivative of power with respect to projected area and solid angle, dF/(dA·dO) . The units are typically watts per square meter per steradian (W/m 2 /sr). The radiance of an extended source (a non-point source or a source whose maximum dimension is less than 1/10 the distance from which the source is observed) is invariant with viewing distance. The radiance of a Lambertian diffuser is invariant with viewing angle because the reduced power reflected off axis is balanced by a reduction in projected area.

Photometry

The concepts defined in the previous section for radiometry have direct equivalents in photometry. The formal difference between these two fields, as stated previously, is that photometry is strictly limited to those wavelengths of energy to which the human observer is sensitive (what is commonly referred to as light). Radiometry is the science of measuring any form of EM radiation.

Luminous intensity ( I v ) is the time rate of flow of light (visual power) emitted by a point source in a given direction. The SI unit for luminous intensity is the candela (cd). Specifically, the candela is the luminous intensity, in a given direction, of a point source that emits monochromatic radiation at a wavelength of 555 nm (5.4 × 10 14 Hz) and that has a radiant intensity in that direction of 1/683W/sr. The specific wavelength was chosen since it is at this wavelength that the human observer has peak photopic sensitivity. A point source whose luminous intensity is 1 cd emits 1 lumen into 1 sr of solid angle.

The candela was originally based on the light emission from the flame of a candle. Over time, the definition has changed dramatically. The unit of measurement was later defined as the light emitted from flame lamps, carbon filament incandescent lamps, and molten platinum. This proved unsuitable for many reasons; a few of which were the difficulty in constructing platinum blackbodies, the susceptibility of platinum to contamination resulting in an uncertainty associated with the melting point of platinum (2042 K), and the fact that the relative spectral radiance changes drastically over the visible portion of the spectrum. The choice of the 1/683 W/sr, while appearing arbitrary, is consistent with the previous definition of the emission from a 1/60 cm 2 of platinum source at its solidification temperature.

The definition for the candela given above indicates that this fundamental SI unit is no longer necessary as it is defined in terms of another fundamental SI unit, the watt. It is, however, still formally defined and in use in the field of photometry.

Luminous flux (Fv) is defined as the flow of light (visual power) emitted by a point source in all directions in space. If a source emits uniformly in all directions, the luminous flux from this source is equal to the product of the source’s luminous intensity multiplied by 4?, the number of steradians in a sphere, namely

F v = I v ·4p

This quantity’s unit of measure, the lumen (lm), as stated previously, is the luminous flux into a solid angle of 1 steradian emitted by a source whose luminous intensity is 1 candela.

Most real world sources do not emit uniformly in all directions, and as such, the relationship between candelas and lumens is empirical. To measure the total flux (lumens), the luminous intensity is measured is as many directions in space as possible using a goniophotometer. These measurements are then integrated numerically, in solid angle space, to arrive at the total flux.

Since most sources are directional in nature, the measure of lumens (luminous flux) may often prove to be misleading. As many applications are concerned with the amount of light falling on a specific object in a specific direction, it is often more informative to measure the candelas (luminous intensity) falling in that direction. The bulbs that we use every day in lamps in our households are typically specified in terms of lumens. It is usually to your advantage to purchase a bulb with high lumens and low power consumption (low wattage) and long life expectancy.

The inconsistency of these two photometric terms often serves as a point of confusion, and possible error, to users. While a bare tungsten filament and a fluorescent bulb may both exhibit the same intensity in a given direction, the visual power is spread over a much larger area in the fluorescent bulb. This gives rise to the photometric term of luminance.

Luminance (Lv) for a source is given by the quotient of the luminous intensity and the projected area of the source in a given direction. The units are typically given as candelas per square meter (cd/m 2 ) or lumens per square meter per steradian (lm/m 2 /sr). The units for this quantity often are referred to by a special name, the nit. This quantity is most often used to refer to the “brightness” of a flat emitting or reflecting surface such as a laptop computer screen.

Luminance is the property of visual power that most closely correlates with perceived brightness. Perceived brightness is not a very reliable measure due to the adaptive and contrast enhancing nature of the human visual system. It is for this reason that reflected-light meters are used to quantify luminance in many photographic applications.

Reflected-light meters measure the luminance of a scene. A scene can be considered to be an infinite number of individual point sources, each the result of light reflected from every element in the scene. These meters will measure the average luminance within the meter’s field of view. Typical acceptance angles for these meters are in the neighborhood of 25 degrees or 1 degree in the case of a spot meter.

Illuminance ( E v ) is a measure of the visual power per unit area incident on a surface. The SI unit for this quantity is the lux and is specified in terms of lumens per unit area. The lux is the number of lumens incident on a 1 m 2 surface 1m distant from the source. Other common units used to specify illuminance are the foot-candle or the phot (see Table 7).

Illuminance is a function of source intensity, the distance from the source to the surface, and the angle at which the light strikes the surface. Illuminance from a point source falls off at a rate proportional to the square of the distance to the source, namely Illuminance from a point source at an angle q from the surface normal is reduced further because the power is spread over a larger area on the surface. The fall off with angle obeys the cosine law

E v (?)=E v (0°) · cos(?)

where E v (0°) is the normal illuminance.

Photographic exposure ( H ) is defined as the product of image-plane illuminance and the exposure duration

H =E v (0°) · t

and is usually given in lux seconds (lux s).

So-called incident light meters measure the power per unit area falling on a surface and are therefore a type of illuminance meter. Note, however, that many meters designed for use in determining photographic exposure are not filtered to match the spectral sensitivity of the standard photopic observer (the CIE V(l) function). Consequently, they may not indicate true illuminance as defined.

Color Temperature

One last topic that will be discussed is that of color temperature. As we mentioned previously, the spectral power distribution of the source illuminating a scene is combined with the spectral reflectance characteristics of a scene element and the spectral response function of the detector material used to determine the amount of sensed energy, either as a spectral radiance measurement (as in the case of a spectroradiometer) or as a band integrated value (as in the case of a light meter). The source of irradiance or illuminance falling onto the scene element therefore warrants attention.

Some light is said to be “warmer” than others. What does this mean? Typically, when light appears to be warmer, it tends to have a greater red component. We previously looked at the blackbody radiance equation that computed the spectral radiance for a blackbody source at a particular temperature and wavelength. Figure 72 shows the spectral radiance produced by a theoretical blackbody source at 6000K (sunlight) and at 2875K (household tungsten lamp).

It is immediately evident that a 3200K source produces significantly more energy at the longer wavelength end of the spectrum. For this reason, objects illuminated with energy at this “color temperature” appear redder than if they were illuminated by a source at 5500K. The flat shape of the curve for a 5500K source implies relatively equal amounts of energy in each portion of the spectrum, which implies that the light is “white” in nature. The 12,000K curve represents midday skylight (which may have a color temperature within the range 9500 to 30,000K, depending on the time of day and season). This curve indicates that the illuminant will appear quite blue for those objects photographed in shadowed areas.

While images taken under tungsten illuminance are often said to be warmer than those taken under daylight illuminance, it is clear that this is not “reflected” in the temperatures of the sources. For this reason, another unit is often used when measuring color temperature, the mired (micro reciprocal degrees). The mired is simply computed as the reciprocal of the temperature in Kelvin times 1,000,000. This scale has two advantages: (1) as the value increases, the illuminant appears warmer; and (2) interval changes in the value on the mired scale result in proportional changes in color. This second point addresses the issue that the same change in color temperature expressed on the Kelvin scale results in disproportionate changes in illuminant color. A change of 1000K at low color temperature is much more significant than this same change for a high color temperature source.

Color Temperature Meters

There are a number of meters on the market that have the specific function of measuring the color temperature of the incident illuminant with the purpose of selecting the proper color correction (CC) filter. Color correction filters are typically blue or amber in color, which raise or lower the color temperature, respectively. The Kodak series of Wratten filters is designed to adjust color temperature. The 81 and 85 series are amber in color and the 80 and 82 series are blue in color. These series of filters have a letter designator that indicates the relative strength of each filter for changing the color temperature. The color temperature scale, mired scale, and correction filters required are illustrated below for use with a daylight color-balance film.

In general, color temperature meters available on the market today are comprised of three silicon photodiodes filtered for red, green, and blue sensitivities appropriate for color film. These devices measure the relative amount of energy present in these three wavelength regions and determine the color temperature based on the shape of the black-body curve that best fits through these metered readings.

Color temperature meters report back to the photographer either the observed color temperature or the mired deviation or the proper Wratten filter number required to achieve
a proper color balance under the current illumination with respect to the desired color temperature. These meters typically allow the user to set the reference color temperature for the particular film they are using (daylight balanced to 5500K, tungsten-A balanced to 3400K, and tungsten-B balanced to 3200K). Many of these meters are capable of measuring either ambient or strobe illumination, or the combination of the both sources.

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