# The Power of Light

### Quantum Theory

The watt (W), the fundamental unit of optical power, is defined as a rate of energy of one joule (J) per second. Optical power is a function of both the number of photons and the wavelength. Each photon carries an energy that is described by Planck’s equation:

Q = hc / λ

Q is the photon energy (joules), h is Planck’s constant (6.623 x 10-34 J s), c is the speed of light (2.998 x 108 m s-1), and λ is the wavelength of radiation (meters). All light measurement units are spectral, spatial, or temporal distributions of optical energy. As you can see in figure 2.1, short wavelength ultraviolet light has much more energy per photon than either visible or long wavelength infrared.

Since silicon photodiodes are more sensitive to light at the red end of the spectrum than to light at the blue end, radiometric detectors filter the incoming light to even out the responsivity, producing a “flat response”. This is important for accurate radiometric measurements, because the spectrum of a light source may be unknown, or may be dependent on operating conditions such as input voltage.

Most sources are continuums, emitting over a broad band of the spectrum. Incandescent lamps are a good example. The color temperature and output of these lamps vary significantly with input voltage. Flat response detectors measure only output power in watts, taking into consideration light at every wavelength.

Another approach is to use a narrow band filter to measure only within a small wavelength band. This is acceptable if the lamp has been fully characterized and the color temperature is carefully monitored. The difficulty with narrow band measurements, however, is that they only look at a single wavelength. If, for example, the color temperature of a lamp changes, it means that the energy distribution has shifted to a different peak wavelength. Single wavelength measurements do not reflect the total output power of the source, and may mislead you into adjusting the source.

Ratios between two narrow bands are quite useful, however, in monitoring color temperature. By measuring the red to blue ratio of a lamp, you can carefully monitor and adjust its spectral output.

The lumen (lm) is the photometric equivalent of the watt, weighted to match the eye response of the “standard observer”. Yellowish-green light receives the greatest weight because it stimulates the eye more than blue or red light of equal radiometric power:

1 watt at 555 nm = 683.0 lumens

To put this into perspective: the human eye can detect a flux of about 10 photons per second at a wavelength of 555 nm; this corresponds to a radiant power of 3.58 x 10-18 W (or J s-1). Similarly, the eye can detect a minimum flux of 214 and 126 photons per second at 450 and 650 nm, respectively.

Use of a photopic correction filter is important when measuring the perceived brightness of a source to a human. The filter weights incoming light in proportion to the effect it would produce in the human eye. Regardless of the color or spectral distribution of the source, the photopic detector can deliver accurate illuminance and luminance measurements in a single reading. Scotopic vision refers to the eye’s dark-adapted sensitivity (night vision).

Effective irradiance is weighted in proportion to the biological or chemical effect that light has on a substance. A detector and filter designed with a weighted responsivity will yield measurements that directly reflect the overall effect of an exposure, regardless of the light source.

Figure 2.4 shows the ACGIH spectral weighting function for actinic ultraviolet radiation on human skin, which is used to determine UV hazard. The threshold limit value peaks at 270 nm, representing the most dangerous segment of the UV spectrum. The harmful effect at 270 nm is two times greater than at the 254 and 297 nm mercury lines, and 9000 times greater than at the 365 nm mercury line.

The outlying extremes of the bandwidth are important to consider as well. If, for example, you are trying to assess the effective hazard of a UVA tanning lamp, which puts out most of its energy in the near UV and visible, you would want a fairly accurate match to the ACGIH curve up to the visible region of the spectrum.

Effective irradiance techniques are also used in many industries that employ UV cured inks, resins, and photoresists. A detector / filter combination is chosen that matches the chemical action spectrum of the substance that is being cured.

Request Light Management Handbook as PDF (ALL Chapters)

Chapter 2 - The Light Measurement Handbook

No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the copyright owner. Requests should be made through the publisher.

Technical Publications Dept.
International Light Technologies
10 Technology Drive
Peabody, MA 01960

ISBN 0-9658356-9-3
Library of Congress Catalog Card Number: 97-93677

Explore more light measurement resources