Letter: Scaling rules for pico-projector laser safety Edward Buckley Abstract — This letter presents a set of scaling rules for the laser safety analysis of scanned-beam and LCOS projection systems, providing a simple method for determining the impact of changes in key system parameters upon the maximum eye-safe luminous flux. Keywords — Laser safety, pico-projector. DOI # 10.1889/JSID19.4.311 1 Introduction Laser-projection systems are classified by wavelength and maximum output power into four classes according to their ability to produce damage in exposed individuals, ranging from Class 1 (which represents no hazard during normal use) to Class 4 (severe hazard for eyes and skin). A given laser safety classification is defined by an Acceptable Emission Limit (AEL), which is dependent upon a number of physi- ological and technology-specific factors and is expressed as a maximum power in Watts (W) or energy in Joules (J) that can be emitted in an exposure time at a given wavelength. As prescribed by the IEC 60825-1 standard, 1 the AEL for visible-wavelength laser safety classification is deter- mined by measuring in a limiting aperture of radius 7 mm, representative of the maximum dilation of the human eye, at a distance of 100 mm from the projection aperture. By determining the maximum permissible optical power in the limiting aperture that a given laser safety classification allows, then inferring the total radiometric projected image power P image which would result in this condition, the maxi- mum luminous flux L max can be derived at a given white point. Eye-safety analyses following this methodology were recently presented for laser-based scanned-beam 2 and LCOS 3 pico-projectors, and maximum radiometric and photometric eye-safe powers and luminous flux values were derived for Class 1 and 2 operation. In this letter, we use the results of these studies to derive a useful set of scaling rules that allow the simple determination of changes in maximum lumi- nous flux output as a function of key system parameters such as projection angles, frame rate, resolution, and wavelength. 2 Photometric power calculation To determine the maximum photometric power, or lumi- nous flux, output L max given the radiometric power limit P max determined from IEC 60825-1, we note that the white- balanced radiometric power P max and white-balanced photometric power L max can be expressed as (1) where the subscripts r, g, and b denote the red, green, and blue components, respectively. To determine the proper weighting of luminous flux components, we first determine the radiometric powers required from each of the laser sources at a given white point. If a matrix M is defined, con- taining the color-matching function 4 values x(λ), y(λ), and z(λ) evaluated at each primary λ r , λ g , and λ b such that (2) and a vector W contains the white point chromaticity values x w , y w , and z w (3) then the relative red, green, and blue radiometric powers at the white point W are given by (4) and the luminous efficacy at a given white point v w is (5) where are the normalized radiometric power contribu- tions at the white point W, v(λ) are the luminous efficacy function evaluated at wavelengths λ. The relationship between the radiometric power output P max and the corresponding white-balanced luminous flux L max is then simply given by (6) The color-matching functions x(λ), y(λ), and z(λ) are plotted as a function of wavelength λ in Fig. 1. For Class 1 classification, we additionally assert a pho- tochemical hazard power limit P ph at the blue and green wavelengths λ b and λ g such that P b  P ph (λ b ) and P g  P ph (λ g ). P P P P L L L L r g b r g b max max , , = + + = + + M = L N M M M O Q P P P x x x y y y z z z r g b r g b r g b ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) l l l l l l l l l W x y z W W W = L N M M M O Q P P P , $ () P l P M W () l= -1 n l l l W = Â $ ()(), P v $ () P l L P W max max . =n Received 12-14-2010; accepted 01-30-2011. The author can be reached at P.O. Box 7483, Jackson WY 83002 USA; telephone 719/271-3939, e-mail: ebuckley@ieee.org. © Copyright 2011 Society for Information Display 1071-0922/11/1904-0311$1.00. Journal of the SID 19/4, 2011 311