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How Light Shaping Diffusers Work

LSD® diffuser films are passive, weakly diffracting, optical components with random (non-periodic) holographic surface relief patterns that perform spectral and angular redistribution of energy carried by wavefronts of coherent sources (like lasers) and partially coherent sources (like cold cathode fluorescent tubes and light emitting diodes). The light intensity from a source is redistributed, along the 3D microstructure surface of the LSD® film, by changing both the amplitude and phase of each local wavefront creating a statistical ensemble of micro-diffraction profiles in the far-field. The intensity from all the individual micro-diffraction distributions combine to produce the final illumination footprint. These components are fabricated using patented holographic exposure techniques involving laser recording of sub-micron speckle features in photosensitive materials. The size and orientation of the speckles can be custom tailored to meet brightness, uniformity, and viewing angle requirements for a given application. These fully randomized (non-periodic) microstructures produce high quality homogeneous light, are non-wavelength dependent, and eliminate moiré (color fringing) without chromatic aberration.

Lighting Design Basics

Photometric Units

A schematic representation depicting the relationship of commonly employed photometric units is shown in the figure below. Solid angle shown represents one steradian

1 Candela [Lm/Sr]	=	the luminous intensity of 1/60 of 1 cm2 of the projected area of a black body radiator operating at the temperature of the solidification of platinum (2045 K)
1 Lumen [Lm]	=	the luminous flux contained within one steradian of solid angle from a source whose luminous intensity is one Cd.
1 Lux [Lm/m²]	=	the illuminance resulting from the flux of one Lumen falling onto a one m2 surface area
1 Nit [Cd/m²]	=	the luminance (brightness) from a source whose luminous intensity is one Candela per projected one m2 surface area normal to the line of observation

Useful Conversions

	Lux	FootCandle	Phot	nit	Cd/ft2	Lambert
Lux	1	0.093	1x10-4
FootCandle	10.764	1	0.001
Phot	1x104	929	1
nit				1	0.093	3.142x10-4
Cd/ft2				10.764	1	0.003
Lambert				3183	295.7	1

Conservation Of Radiance

The design of any illumination system is based on the fundamental principle that it is physically impossible for the final radiance (brightness) at the image to exceed the initial radiance of the source. Consider the illumination system shown in the figure below which is assumed to have no optical loss.

The incremental flux, d²Φ, radiated by dA₁ = dx₁ dy₁ into an element of solid angle dΩ₁ = sin θ₁ dθ₁ df at the entrance pupil of the illumination system is given by

d²Φ = B₁(θ₁, ø) dA₁ sin θ₁cosθ₁ dθ₁ dø

If the system is truly lossless, this incremental flux must pass through an area element dA₂ = dx₂ dy₂ in image space from a solid angle dΩ₂ = sin θ₂ dθ₂ dø, and thus the image radiance in this direction is given by

B₂(θ₂, ø) = d²Φ ⁄ (dA₂ sin θ₂ cosθ₂ dθ₂ dø)

Because the optics of the illumination system are assumed to be lossless all rays passing through must satisfy the Abbe sine theorem

N₁dx₁ sin θ₁ = N₂ dx₂ sin θ₂

And by changing x to y and differentiating

N₁dy₁ cos θ₁ dθ₁ = N₂ dy₂ cos θ₂ dθ₂

Combining these last three equations results in the general statement of the radiance theorem for an image

B₁(θ₁, ø) / N₁² Ξ B₂(θ₁, ø) ⁄ N₂²

Thus no illumination system can produce an image brightness that is greater than that of the initial source.

Entendué

If an illumination system were perfectly transmitting in the sense that all of its components neither absorb nor reflect and that all rays entering the system exit without encountering any limiting stops or apertures, then the total flux collected by the system is given by

Φ = ∫∫ d²Φ

= ∫∫ B(r, n) dA cos θ dΩ

where B(r, n) is the source radiance at the point r in the direction of the unit vector n, where the area integral (Fourier area) extends over that portion of the surface of the source which lies within the entrance window and where the angular integral extends over the solid angle subtended by the entrance pupil of the illumination system from the location r as shown in the figure below.

For example, a Lambertian source with radiance B₀ has a total flux given by

Φ = B0 ∫∫ dA cos θ dΩ

which can be expressed as

Φ = B₀ ε ⁄ N02

where the entendué of the system is defined as

ε = N₀² ∫∫ dA cos θ dΩ

For integrated lighting systems the entendué is a purely geometrical quantity that measures the flux-gathering capabilities of a system in that the collected flux is given by the product of this quantity with the basic radiance of the source. For a lossless illumination system the entendué is invariant between the source and image planes. That is to say no system of external optics can increase the entendué of an illumination system (i.e. it is not possible to get out more light output than what you started with). Therefore evaluating the performance of an integrated lighting system design requires an understanding of the change in the entendué at various locations as the light propagates through the various secondary optics and diffusers.

For details on any Luminitco product, visit the Luminitco.com OnLine Catalog. For more information or custom requests, call 800-448-3572