optical radiation safety considerations
Optical radiation safety considerations

This document outlines the basic principles underlying the proper use of the optical radiation safety calculator. It is designed for assessing situations in which the eye is illuminated, either to provide a stimulus or to illuminate it for photography, videography or direct observation. The optical radiation safety calculator performs calculations for radiation at visible wavelengths (400-700 nm), and near infrared (700-1400 nm).

1. Radiometry basics
2. Types of ocular exposure
3. Using the program
4. Glossary
5. References

1. Radiometry basics

The basic principles of radiometry can be found elsewhere (link to W&S ref), but will be presented here in brief. Measurements can be made either in terms of radiometric units, which correspond to raw energy or power, or photometric units, which are corrected for visibility. When dealing with safety issues, we are primarily concerned with radiometric measures; the same principles apply to photometric measurements, however, so when we use a radiometric term, the corresponding photometric term will be listed in parentheses.

The basic radiometric (photometric) measurements are irradiance (illuminance) and radiance (luminance). Irradiance describes the total power falling on a surface (such as the surface of a detector, or a tissue surface in the eye). The units of irradiance are expressed in power per unit area, typically Watts per centimeter squared (W/cm²).

When a surface is irradiated with a certain amount of power, the energy comes from a source. Most sources are distributed in space, that is, they have some finite size. (This size approaches zero for a perfectly collimated beam, such as might be emitted by a laser.) The radiance of a source is simply the irradiance it produces, divided by the size of the source, where the size is expressed as the solid angle (in steradians) subtended by the source from the point at which the measurement is made. A little reflection should make it clear that the radiance of a source is independent of the distance at which the measurement is made: if we double the distance from the source, the irradiance will decrease by a factor of 4 (inverse square law); but the apparent size of the source will also decrease by a factor of 4, and the two factors cancel out.

2. Types of ocular exposure

For considerations of eye safety, there are two principle areas of concern: the first is corneal irradiance. When optical radiation (particularly infrared) strikes the cornea, it can heat and dry it, causing damage to the tissue. (Infrared radiation can also cause damage to soft contact lenses at levels that are considered safe for eye exposure, but to my knowledge there is no published data on this!)

The second area of concern is retinal irradiation. Damage to the retina can cause areas of local blindness ("scotomas"). The calculation of retinal irradiance is fairly straightforward: the total amount of power entering the eye can be calculated as the product of the corneal irradiance times the effective pupil area. The illuminated area of retina will be an image of the source, subtending the same angle from the posterior nodal point as the source does from the anterior nodal point. Therefore, the retinal area is simply the product of the solid angle subtended by the source (in steradians) and the posterior nodal distance of the eye.

To convert retinal irradiance to radiance, we need to divide by the source solid angle; but at the retina, the apparent source is the exit pupil of the eye, so this is the relevant measure. It can be shown by a little algebra that this is identically equal to the original source radiance!

For the calculations we assume that the source is uniform. This assumption may be violated for real sources; for example, a lamp filament will have "hot spots" where the local radiance is higher than the average radiance. In these situations, it is best to use a diffuser to homogenize the source image. Diffractive optical elements capable of diffusing a beam within a narrow angular range (such as those manufactured by Physical Optics Corporation) are ideal for this application.

3. Using the program

Detector diameter.
A circular detector area is assumed. For a circular detector, simply enter the diameter in millimeters of the active surface. For a non-circular detector, calculate the area (in mm²), then divide by pi (3.14159), take the square root of the result and multiply by 2 to obtain the equivalent diameter.

Wavelength
A monochromatic or narrow band source is assumed. For a broadband infrared source, the value here is not too critical, because the calculations are not too wavelength dependent. To be conservative, use a value of xxx nm. Broadband visible sources are more problematic, because the "blue light hazard" function has a sharp peak at 4xx nm.

Source dimensions at pupil
These parameters are most relevant for setups (such as Maxwellian view optical systems) where the source is imaged in the pupil by a system of one or more lenses. In the case where the source image is smaller than the natural pupil (assumed to be 7 mm), the source area is used for the effective pupil area. For cases where the entire eye/face is illuminated directly by a source, the values here do not really matter, as long as they are larger than 7mm.

Apparent size and distance of the source
For free viewing of a source, simply enter the actual size and distance (in millimeters). For Maxwellian view, where the final lens appears uniformly filled with light, use the diameter and distance of the lens.

Detector power
Enter the power measurement in microwatts.

4. Glossary

Effective pupil area: The area of the pupil through which light passes. Under free viewing conditions, this is usually just the area of the natural pupil. It can be smaller than the natural pupil under special conditions, such as viewing through a small artificial pupil, or when using an instrument with a small exit pupil such as a Maxwellian view optical system.

5. References

 Optical Radiation Safety Calculator


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