Reflector-Light Source Requirements for Homogeneous Format illumination in Night Aerial Photography Richard A. Gross

Hycon Manufacturing Company, Monrovia, California. Received 13 September 1965.

When taking aerial photographs at night by use of a light source aboard an aircraft, it is most desirable to illuminate a (uniform) target in such a way that it will reflect equal amounts of light energy from all points, in order to illuminate uniformly a film. I t is also desirable to do this with the least amount of power.

In order to fulfill these requirements, a light source with a specially designed reflector is necessary. In this letter, the power required for a lamp used with this type of reflector is determined, and a basic design requirement for the geometry of the reflector is constructed.

Consider a light source of luminous intensity I0(θ, ) lm/sr with θ, angles represented in Fig. 1. About this light source consider a reflector that has the effect of redistributing the light from the source. The effect of the reflector is represented by the unitless operator G(θ, ). The source-reflector unit thus has an effective intensity of G(θ, )I0(θ, ). Define a differential solid angle dγ into which the unit radiates by a differential target area and the distance to it from the unit. The flux to this differential area is then

From Fig. 2, it can be noted tha t dγ = n . dA/r2. Since

we have

then

Assume the ground a perfectly diffusing surface. Then we have the intensity of any differential area in the target dIT(θ, ) = (dΦ0/π) cos ξ; thus, the equation is

The camera lens of area σ defines a small solid angle ω at the center of the differential area:

672 APPLIED OPTICS / Vol. 5, No. 4 / April 1966

Fig. 1. Geometry of solid angle dγ.

Fig. 2. Geometry of solid angle ω.

Fig. 3. Target format geometry.

or

The flux from the differential area incident on the lens is dΦL = ωdIT, or

This flux falls on the area dXdY, corresponding to the area dxdy of the target. From Fig. 3 we see that dX = (f/h)dx and, sim­ilarly, dY = (f/h)dy. With dx = h sec2θdθ and dy = hsec2 d , we obtain dXdY = f2 sec2θ sec2 dθd .

The film illumination is therefore

This function describes, for a given lens and altitude, the varia­tion of illumination across the (square) format. However, we have not yet defined G(θ, ) , which describes the effect of the reflector and can be made to cause the illumination ΕΡ(θ, ) to be independent of θ or .

First let us separate I0(θ, ) into a flux amplitude F0 (lm) and an angular distribution function β(θ, ) percent/sr. Then we derive I0(θ, ) = F0β(θ, ). Equation (1) becomes

I t is obvious that in order to illuminate the format uniformly, the function EF(θ, ) must be independent of θ or . Thus, let

This defines, to within a constant, the function G(θ, ):

The reflector operator must have this form if the format is to be illuminated uniformly. Assuming a reflector can be designed to produce this operator, the illumination of the format becomes:

a t any position of the format. In the term C, the reflectivity of the reflector and the flux blocked by the electrical connections to the lamp and mechanical supports must be taken into account.

In order to cause all the light from the source-reflector unit to fall on the target area only, we must insist tha t

We see, then, tha t C must be a function of the target limits and 0:

On integrating, it is found tha t

If we express explicitly the reflectivity of the reflector ρ, the fraction η of flux not blocked by supports and connectors, the transmissivity of the atmosphere T and of the lens τ, and the terrain albedo α, we obtain, instead of Eq. (3),

The total flux F0 required for a lamp is determined by film sensitivity. If the required exposure J for a specific density is Et meter-candle-seconds (lm-sec/m2), where E is the illumination exposing the film for t seconds, E = J/t must equal EF) and thus the flux required is

If the lamp has a luminous efficiency of ε lm/W, the lamp re­quires P0 = F0/ε W.

[The value of [C(θ0, 0)]-1 is determined from Eq. (4)]. This is the power required for a lamp-reflector unit satisfying

both the condition of uniform format illumination, and total use of the lamp's flux output. In order to enable us to use this small amount of power, a reflector must be designed which redistributes the source-flux according to Eq. (2). Sample calculations indi­cate reduction of power requirements of hundreds of times for lamps used with this type of reflector compared to those without any reflector.

April 1966 / Vol. 5, No. 4 / APPLIED OPTICS 673