Spectroradiometers are devices designed to measure the spectral power distribution of a source. From the spectral power distribution, the radiometric, photometric, and colorimetric quantities of light can be determined in order to measure, characterize, and calibrate light sources for various applications.

Spectroradiometers typically take measurements of spectral irradiance and spectral radiance. This spectral data can be used to calculate CIE tristimulus values through mathematical integration. CIE chromaticity coordinates and luminosity can then be calculated, providing a complete description of the source’s color, including chromaticity, spectral power, illuminance, and luminance.[1] Spectroradiometers are stand-alone systems that work independently without the need to be connected to a PC. This makes them highly portable while maintaining the accuracy of a spectrometer.[2]

## Background

The field of spectroradiometry concerns itself with the measurement of absolute radiometric quantities in narrow wavelength intervals.[3] It is useful to sample the spectrum with narrow bandwidth and wavelength increments because many sources have line structures [4] Most often in spectroradiometry, spectral irradiance is the desired measurement. In practice, the average spectral irradiance is measured, shown mathematically as the approximation:

${\displaystyle E(\lambda )={\frac {\Delta \Phi }{\Delta A\Delta \lambda }}}$

Where ${\displaystyle E}$ is the spectral irradiance, ${\displaystyle \Phi }$ is the radiant flux of the source (SI unit: watt, W) within a wavelength interval ${\displaystyle \Delta \lambda }$ (SI unit: meter, m), incident on the surface area, ${\displaystyle A}$ (SI unit: square meter,m²). The SI unit for spectral irradiance is W/m3. However it is often more useful to measure area in terms of centimeters and wavelength in nanometers, thus submultiples of the SI units of spectral irradiance will be used, for example μW/cm2*nm[5]

Spectral irradiance will vary from point to point on the surface in general. In practice, it is important note how radiant flux varies with direction, the size of the solid angle subtended by the source at each point on the surface, and the orientation of the surface. Given these considerations, it is often more prudent to use a more rigorous form of the equation to account for these dependencies[5]

Note that the prefix “spectral” is to be understood as an abbreviation of the phrase “spectral concentration of” which is understood and defined by the CIE as the “quotient of the radiometric quantity taken over an infinitesimal range on either side of a given wavelength, by the range”.[6]

## Spectral power distribution

The spectral power distribution (SPD) of a source describes how much flux reaches the sensor over a particular wavelength and area. This effectively expresses the per-wavelength contribution to the radiometric quantity being measured. The SPD of a source is commonly shown as an SPD curve. SPD curves provide a visual representation of the color characteristics of a light source, showing the radiant flux emitted by the source at various wavelengths across the visible spectrum[7] It is also a metric by which we can evaluate a light source’s ability to render colors, that is, whether a certain color stimulus can be properly rendered under a given illuminant.

Characteristic spectral power distributions (SPDs) for an incandescent lamp (left) and a fluorescent lamp (right). The horizontal axes are in nanometers and the vertical axes show relative intensity in arbitrary units.

## Sources of error

The quality of a given spectroradiometric system is a function of its electronics, optical components, software, power supply, and calibration. Under ideal laboratory conditions and with highly trained experts, it is possible to achieve small (a few tenths to a few percent) errors in measurements. However, in many practical situations, there is the likelihood of errors on the order of 10 percent [5] Several types of error are at play when taking physical measurements. The three basic types of error noted as the limiting factors of accuracy of measurement are random, systematic, and periodic errors [8]

Random errors are variations about that mean. In the case of spectroradiometric measurements, this could be thought of as noise from the detector, internal electronics, or the light source itself. Errors of this type can be combated by longer integration times or multiple scans.

Systematic errors are offsets to the predicted “correct” value. Systematic errors generally occur due to the human component of these measurements, the device itself, or the setup of the experiment. Things such as calibration errors, stray light, and incorrect settings, are all potential issues.

Periodic errors arise from recurrent periodic or pseudo-periodic events. Variations in temperature, humidity, air-motion, or AC interference could all be categorized as periodic error.[8]

In addition to these generic sources of error, a few of the more specific reasons for error in spectroradiometry include:

• The multidimensionality of the measurement. The output signal is dependent on several factors, including magnitude of measured flux, its direction, its polarization, and its wavelength distribution.
• The inaccuracy of measuring instruments, as well as the standards used to calibrate said instruments, cascaded to create a larger error throughout the entire measurement process, and
• The proprietary techniques for reducing multidimensionality and device instability error.[5]

Gamma-scientific, a California-based manufacturer of light measurement devices, lists seven factors affecting the accuracy and performance of their spectroradiometers, due to either the system calibration, the software and power supply, the optics, or the measurement engine itself.[9]

## How it Works

The essential components of a spectroradiometric system are as follows:

• Input optics that gather the electromagnetic radiation from the source.
• A monochromator, separating light into its component wavelengths
• A detector
• A control and logging system to define data and store it.[10]
Input optics

The front-end optics of a spectroradiometer includes the lenses, diffusers, and filters that modify the light as it first enters the system. The material used for these elements determines what type of light is capable of being measured. For example, to take UV measurements, quartz rather than glass lenses, optical fibers, Teflon diffusers, and barium sulphate coated integrating spheres are often used to ensure accurate UV measurement.[10]

Monochromator
Main article: monochromator
Diagram of a Czerny-Turner monochromator.

To perform spectral analysis of a source, monochromatic light at every wavelength would be needed to create a spectrum response of the illuminant. A monochromator is used to sample wavelengths from the source and essentially produce a monochromatic signal. It is essentially a variable filter, selectively separating and transmitting a specific wavelength or band of wavelengths from the full spectrum of measured light and excluding any light that falls outside that region.[11]

A typical monochromator achieves this through the use of entrance and exit slits, collimating and focus optics, and a wavelength-dispersing element such as a diffraction grating or prism.[8] Modern monochromators are manufactured with diffraction gratings, and diffraction gratings are used almost exclusively in spectroradiometric applications. Diffraction gratings are preferable due to their versatility, low attenuation, extensive wavelength range, lower cost, and more constant dispersion.[11] Single or double monochromators can be used depending on application, with double monochromators generally providing more precision due to the additional dispersion and baffling between gratings.[10]

Detectors
Photomultiplier

The detector used in a spectroradiometer is determined by the wavelength over which the light is being measured, as well as the required dynamic range and sensitivity of the measurements. Basic spectroradiometer detector technologies generally fall into one of three groups: photoemissive detectors (e.g. photomultiplier tubes), semiconductor devices (e.g. silicon), or thermal detectors (e.g. thermopile).[12]

The spectral response of a given detector is determined by its core materials. For example, photocathodes found in photomultiplier tubes can be manufactured from certain elements to be solar-blind – sensitive to UV and non-responsive to light in the visible or IR.[13]

Control and logging system

The logging system is often simply a personal computer. In initial signal processing, the signal often needs to be amplified and converted for use with the control system. The lines of communication between monochromator, detector output, and computer should be optimized to ensure the desired metrics and features are being used.[10] The commercially available software included with spectroradiometric systems often come stored with useful reference functions for further calculation of measurements, such as CIE color matching functions and the V${\displaystyle \lambda }$ curve.[14]

## Applications

Spectroradiometers are used in many applications, and can be made to meet a wide variety of specifications. Example applications include:

• Solar UV and UVB radiation
• LED measurement
• Display measurement and calibration
• CFL testing
• Remote detection of oil slicks[15]

Plant research and development [16]

## References

1. ^ IES, Illuminating Engineering Society. Lighting Measurements: A Basic Approach to Understanding the Principals of Lighting Science. Handour. Comp. Nlena and Associates, Inc. Retrieved from http://www.ies.org/pdf/education/IES-Color-3-Webcast-Handout.pdf
3. ^ Leslie D. Stroebel and Richard D. Zakia (1993). Focal Encyclopedia of Photography (3rd ed. ed.). Focal Press. p. 115. ISBN 0-240-51417-3
4. ^ Berns, Roy S. "Precision and Accuracy Measurements." Billmeyer and Saltzman's Principles of Color Technology. 3rd ed. New York: John Wiley & Sons, 2000. 97-100. Print
5. ^ a b c d Kostkowski, Henry J. Reliable Spectroradiometry. La Plata, MD: Spectroradiometry Consulting, 1997. Print.
6. ^ Sanders, Charles L., and R. Rotter. The Spectroradiometric Measurement of Light Sources. Paris, France: Bureau Central De La CIE, 1984. Print.
7. ^ GE Lighting. "Learn About Light: Spectral Power Distribution Curves: GE Commercial Lighting Products." Learn About Light: Spectral Power Distribution Curves: GE Commercial Lighting Products. N.p., n.d. Web. 10 Dec. 2013. <http://www.gelighting.com/na/business_lighting/spectral_power_distribution_curves/>
8. ^ a b c Schnedier, William E., and Richard Young, Ph.D. Spectroradiometry Methods. Application Note (A14). N.p., 1998. Web. <http://biology.duke.edu/johnsenlab/pdfs/tech/spectmethods.pdf>
9. ^ Gamma Scientific. "Seven Factors Affecting Spectroradiometer Accuracy and Performance." Gamma Scientific. N.p., n.d. Web. <http://www.gamma-sci.com/spectroradiometer-accuracy-performance/>.
10. ^ a b c d Bentham Instruments Ltd. A Guide to Spectroradiometry: Instruments & Applications for the Ultraviolet. Guide. N.p., 1997. Web. <http://www.bentham.co.uk/pdf/UVGuide.pdf>
11. ^ a b American Astronomical Society. "Study Notes: AAS Monochromator." Study Notes: AAS Monochromator. N.p., n.d. Web. 2013. <http://toolboxes.flexiblelearning.net.au/demosites/series5/508/Laboratory/StudyNotes/snAASMonochrom.htm>.
12. ^ Ready, Jack. "Optical Detectors and Human Vision." Fundamentals of Photonics (n.d.): n. pag. SPIE. Web. <http://spie.org/Documents/Publications/00%20STEP%20Module%2006.pdf>.
13. ^ J. W. Campbell, "Developmental Solar Blind Photomultipliers Suitable for Use in the 1450–2800-Å Region," Appl. Opt. 10, 1232-1240 (1971) http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-10-6-1232
14. ^ Apogee Instruments. Spectroradiometer PS-100 (350 - 1000 Nm), PS-200 (300 - 800 Nm), PS-300 (300 - 1000 Nm). N.p.: Apogee Instruments, n.d. Apogee Instruments Spectroradiometer Manual. Web. <http://www.apogeeinstruments.com/content/PS-100_200_300manual.pdf>.
15. ^ Mattson, James S., Harry B. Mark, Jr., Arnold Prostak, and Clarence E. Schutt. Potential Application of an Infrared Spectroradiometer for Remote Detection and Identification of Oil Slicks on Water. Tech. 5th ed. Vol. 5. N.p.: n.p., 1971. Print. Retrieved from <http://pubs.acs.org/doi/pdf/10.1021/es60052a004>
16. ^ McFarland, M and Kaye, J (1992) Chlorofluorocarbons and Ozone. Photochem. Photobiol. 55 (6) 911-929.