DLPA037A June   2013  – August 2025 DLP500YX , DLP5500 , DLP6500FLQ , DLP6500FYE , DLP650LNIR , DLP670S , DLP7000 , DLP7000UV , DLP9000 , DLP9000X , DLP9000XUV , DLP9500 , DLP9500UV

 

  1.   1
  2.   Abstract
  3.   Trademarks
  4. 1Introduction
  5. 2Understanding Diffraction – An Intuitive View
    1. 2.1 Single Slit Diffraction
    2. 2.2 Multiple Slit Diffraction
    3. 2.3 Reflective Diffraction Gratings
    4. 2.4 Extending to Two Dimensional Gratings
    5. 2.5 The DLP© DMD as a Two Dimensional Grating
    6. 2.6 Blaze Formulas
  6. 3Advantages and Considerations
  7. 4Conclusion
  8. 5References
  9. 6Revision History

2.6 Blaze Formulas

Tilt Angle

A blaze chart can be created using the following formula:

Equation 6. θ t i l t n , λ , d , θ i = 1 2 a s i n n λ d 2 - s i n θ i + θ i

where n is the integer order number for the (n,n) order, λ is the wavelength, d is the pixel pitch and θi is the incident angle relative to the DMD array normal.

The blaze chart can be used to determine the range of incident angles that results in an nth order blaze for a given tilt angle range. A blaze condition is not possible for all combinations of parameters. If no real answers to the equation exist, then a blaze condition is not possible for the given parameters.

Anti-Blaze

Using values of n + ½ anti-blaze curves can also be plotted. An anti-blaze occurs when the envelope peak falls centered in the middle of four adjacent orders so that the four orders equally share the energy. These four orders combined have considerbally less energy than a signle blazed order.

Incident Angle

DMDs have a prescribed tilt angle plus or minus a specified range use the following formula to calculate the incident angle (θi) for a blaze conditions:

Equation 7. θ i n , λ , d , θ t i l t =   θ t i l t - a c o s n λ d 2 × 1 s i n θ t i l t

where n is the integer order number for the (n,n) order, λ is the wavelength, d is the pixel pitch and θtilt is the specified tilt angle of the DMD pixels. If no real answers to the equation exist, then a blaze condition is not possilbe for the given parameters.

Littrow Blaze

When the incident light and the reflected light traverse the same path this is known as the Littrow condition. When this condition also co-incides with a blaze condition a Littrow Blaze occurs. Therefore the incident angle and the tilt angle coincide which we label θLittrow. Use this formula for Littrow Blaze:

Equation 8. θ L i t t r o w n , λ , d = a s i n 1 2 n λ d 2

where n is the integer order number for the (n,n) order, λ is the wavelength, and d is the pixel pitch.