An Introduction to Photometry
Photometry is the science concerned with measuring human visual response to light. Because the eye is a highly complex organ, this is by no means a simple task. It involves the meeting of many disciplines: psychology, physiology, and physics among them.
Photometry can be said to have become a modern science in 1924, when the Commission Internationale de l’Eclairage (CIE) met to define the response of the average human eye. The Commission measured the light-adapted eyes of a sizable sample group, and compiled the data into the photopic curve. Simply stated, the curve reveals that people respond strongest to the color green, and are less sensitive to the spectral extremes, red and violet. The eye has an altogether different response in the dark-adapted state, wherein it also has difficulty determining color. This gave rise to a second set of measurements, and the scotopic curve.
Having defined the eye’s spectral response, CIE sought a standard light source to serve as a yardstick for luminous intensity. The first source was a specific type of candle, giving rise to the terms footcandle and candlepower. In an effort to improve repeatability, the standard was redefined in 1948 as the amount of light emitted from a given quantity of melting platinum.
Basic Photometry Concepts
The basic unit of photometry is the lumen, which is related to its radiometric analog, the Watt, by: lm = 683 x W x Vλ.
Where Vλ is the relative luminosity, a coefficient scaled to visual response. Unity occurs at the eye’s peak response wavelength, 555 nanometers.
Two useful laws in photometry recur: the inverse square law and the cosine law. The first defines the relationship between illumination from a constant-intensity light source and its distance from a surface. It states that the intensity per unit-area on the surface varies in inverse proportion to the square of the distance between the source and surface.
Accordingly, successive illuminance measurements are only as accurate as the control of source to surface distance. Further, if illuminance is known at one distance, it can, barring interference, be calculated for any distance.
The cosine law indicates the intensity of light on a surface of a fixed area varies with incident angle. In fact, the intensity falls off as the cosine of the angle. This results because the projected surface area, in the plane perpendicular to incidence, is proportionally reduced.
Thus in measurements of environmental lighting, sensors require cosine correction to account for off-axis light. Without it, considerable errors will occur, especially with bright sources at low incident angles ( windows). This often accounts for the difference in readings between two photometers.
The cardinal challenge in photometry is to recreate the spectral response of the human eye. But electronic sensors have distinct response characteristics which bear no resemblance to the CIE standard observer. Therefore, these sensors must be spectrally corrected. Two techniques are conventionally used to accomplish this: wavelength scanning, and detector/filter matching.
Scanning can be accomplished with discrete-wavelength, scanning monochromators, or multi-channel detectors. In either case, the intensity of a light source is measured wavelength-by-wavelength, and then the results are mathematically fitted to the photopic curve. For this reason, such techniques do not occur in real time, and require microprocessor control. Scanning approaches offer high accuracy, but tend to be costly and complex to operate.
Optical filtering offers a simple and cost-effective solution. With only one photo-current signal to process, single-channel electronics can be used. Also, recent advances in filter design, and improvements in solid-state detectors, allow this method to rival scanning systems for photometric accuracy.
This filter-matching technique involves the layering of colored-glass filters over an optical detector. Each element functions to attenuate selective wavelengths until the detector’s response simulates the CIE curve. Planar diffused silicon photodiodes offer the best photosensor characteristics, since they afford high sensitivity and linearity throughout the visible spectrum.
Using silicon photodetectors, and advanced filter designs, UDT Instruments matches the CIE human eye response curve within 1% total area error. This is the best match achievable, according to CIE.
There is another more important specification of the quality of a photometric detector and that is the f₁, value. This is defined by the CIE and is a numerical value assigned to the average deviation of the photometric detector’s response from the CIE curve. An f₁, < 1.5% is the best possible laboratory grade detector while an f₁, < 3% is considered suitable for most applications. However, the relationship between a given detector and filter is delicate. Once the two have been matched, they should not be interchanged with other photometric detector/filter pairs. Each detector exhibits unique response characteristics that require a specific combination of filter layers and thicknesses.
Once the detector’s response is fixed, it is calibrated using the transfer of standards technique. This requires a detector of known response, which can be obtained from the National Institute of Science and Technology (NIST). A detector/filter pair is positioned before an optical source with constant wave-length and intensity characteristics (usually a tungsten halogen lamp). The electrical output of the detector under test is then compared to the standard detector’s output.
Once the sensor’s luminous response is determined, it can be matched to a precision gain-controlled electronic amplifier and read-out system.
Important Photometry Terms
Luminous flux is expressed in lumens, the fundamental unit of photometry. It is a measure of the total optical output of a visible light source. The measurement requires all of a source’s power to be concentrated on a detector. This can be a problem with divergent sources like LEDs, and lamps. In these cases, integrating spheres are often used.
Illuminance is a measure of the amount of visible light incident upon a prescribed surface area. In English units, one lumen of flux falling on one square foot is termed a footcandle. The metric equivalent, one lumen per square meter, is called a lux (10.76 lux = 1 footcandle).
Of course, detectors don’t have such large areas. So the area of the detector is multiplied proportionally. Special attention is due when the detector is under-filled or used behind corrective optics, since the sensor’s area no longer defines the surface being illuminated.
For example, illuminance measurements are particularly susceptible to errors introduced by off-axis light. So cosine-correcting diffusers are used with the detector head. Since the cosine diffuser is essentially imaged onto the sensor, the diffuser’s area, not the sensor’s, represents the measurement surface.
Luminous exitance is an intrinsic property of a light source. It is calculated by measuring luminous flux (lumens), and dividing by the surface area of the source. This measurement is also expressed in lumens per square meter, but is not to be confused with illuminance measurements or lux. The area referred to in luminous exitance is that of the light source, not the illuminated surface. This measurement is most applicable to emitters with flat surfaces.
Luminous intensity is also a source property, but one where the source’s direction and divergence come into play. Defined as the quantity of luminous flux emitted uniformly into a solid angle, the basic unit of luminous intensity is the candela, equal to one lumen per steradian.
Several things are suggested by this definition. One, this measurement is not applicable to collimated light sources. Two, it is inaccurate for non-uniform emitters. To calculate luminous intensity, the detector’s area (or the area prescribed by the aperture in front of it), and its distance from the light source must be known. From these, the solid angle can be calculated, and then divided into the flux reading.
Luminous energy is a measure of the rate of flow of flux, and so is expressed in lumen-seconds. Generally, it is applied to flashed or pulsed sources.
It is also possible to measure any photometric quantity on a time-dependent basis. For instance, the illuminance of a rotating beacon in one direction could be integrated over time to yield footcandle-seconds.
Also known as photometric brightness, luminance is a measure of the flux reflected by, or emitted from, a relatively flat and uniform surface. The technique takes into account the area of the surface measured, and the angle sub-tended by an observer looking at it.
Luminance may be thought of as luminous intensity per unit area, and so in metric terms is expressed as candelas per square meter. But a host of other terms are used for this measurement, some to describe a circular measurement area rather than a square one.
To measure luminance, the detector field-of-view must be restricted, and its angle calculated. Usually, a lens or baffle is used to achieve this. In fact, the human eye, with its lens and aperture, functions as a luminance meter.
Note that so long as the detector’s field-of-view is filled, this measurement is independent of the distance between the detector and measurement planes. That’s because field size and source intensity vary in direct proportion to one another as a function of distance.
UDT Instruments, a Gamma Scientific company, offers a line of photometer and radiometer components to meet the industrial need for simple, practical, and reliable optical measurements. This line includes a range of optometers, photosensors and photosensor accessories. UDT Instruments offers high-accuracy photometer and radiometer systems based on our TIA-3000 transampedance amplifier technology. These systems deliver state of the art performance to the most exacting clients in research and advanced metrology.
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