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Application NoteDMD Optical Efficiency for Visible Wavelengths

ABSTRACTThe purpose of this document is to summarize the optical properties that are most important in estimating theefficiency of a Digital Micromirror Device (DMD) in a projection system.

Table of Contents
1 Purpose and Scope................................................................................................................................................................ 2
1.1 Limitations.......................................................................................................................................................................... 2
1.2 Acronyms Used in This Document.....................................................................................................................................2
2 On-State Fill Factor.................................................................................................................................................................2
3 Window Properties................................................................................................................................................................. 3
4 Mirror Diffraction Efficiency...................................................................................................................................................3
4.1 Mirror Flatness................................................................................................................................................................... 3
4.2 Mirror Diffraction Efficiency................................................................................................................................................ 3
4.3 Diffraction Efficiency with Mismatched Illumination and Projection f-numbers...................................................................8
5 Mirror Reflectivity................................................................................................................................................................... 9
6 Estimating Overall DMD Efficiency....................................................................................................................................... 9
7 References............................................................................................................................................................................ 10
8 Revision History................................................................................................................................................................... 10

List of Figures
Figure 4-1. Simulated 5.4 µm Pitch DMD Far Field Radiance Image; Dashed Circle Shows Outline of Projection Lens
Aperture Edge.......................................................................................................................................................................... 5
Figure 4-2. Summary of Calculated Average Photopic Diffraction Efficiencies for Different Pixel Sizes (420 nm–680 nm
wavelength)..............................................................................................................................................................................5
Figure 4-3. 13.68 µm Pitch DMD Mirror Calculated Diffraction Efficiency (matched illumination and projection f-numbers)...... 6
Figure 4-4. 10.8 µm Pitch DMD Mirror Calculated Diffraction Efficiency (matched illumination and projection f-numbers)........ 6
Figure 4-5. 9.0 µm Pitch DMD Mirror Calculated Diffraction Efficiency (matched illumination and projection f-numbers).......... 7
Figure 4-6. 7.56 µm Pitch DMD Mirror Calculated Diffraction Efficiency (matched illumination and projection f-numbers)........ 7
Figure 4-7. 5.4 µm Pitch DMD Mirror Calculated Diffraction Efficiency (matched illumination and projection f-numbers).......... 8
Figure 4-8. 7.56 μm Pitch DMD Mirror Calculated Diffraction Efficiency With Matched and Mismatched f-numbers..................8
Figure 5-1. DMD Mirror Typical Reflectivity................................................................................................................................. 9

List of Tables
Table 2-1. DMD On-State Fill Factor............................................................................................................................................3
Table 6-1. Total Photopic Average Efficiency Calculation(1) ......................................................................................................10

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Purpose and Scope

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1 Purpose and Scope
The next three sections discuss the fill factor, window optical properties, and the active mirror array properties,
respectively. This report concludes with a discussion on calculating the overall efficiency.
As discussed in more detail in Section 6, overall optical efficiency can be estimated using
Equation 1.
EfficiencyDMD = transmissionwindow × efficiencyfillfactor × efficiencydiffraction × reflectivitymirror × transmissionwindow

(1)

where
•
•
•
•

transmissionwindow is single-pass window transmission including two anti-reflection surfaces. This term is
accounted for twice because light travels through the window twice.
efficiencyfillfactor is the fractional mirror coverage (on-state mirrors) as viewed from the illumination direction
efficiencydiffraction is the mirror array diffraction efficiency which can include effects of non-flat mirrors
reflectivitymirror is the mirror reflectivity including mirror scatter

Overall DMD efficiency is generally a product of fill factor, window transmission, diffraction efficiency, and mirror
reflectivity, which are described in more detail in the following sections.

1.1 Limitations
This document does not include system-level efficiency losses such as etendue mismatches, which can bebetter assessed using a ray trace model based on the actual optical design. Factors that affect contrast ratio
are also important, however, the interactions are often much more complex requiring rigorous electromagnetic
scattering theory of the optical system, and it would be difficult to summarize all these factors in this type ofreport.

1.2 Acronyms Used in This Document
Abbreviations

Descriptions

DMD

Digital Micromirror Device

AOI

Angle of Incidence

WLP

Wafer Level Package

2 On-State Fill Factor
Table 2-1 shows typical on-state fill factor based on DMD micromirror pitch.
••

2

Tilt angle - Nominal mirror tilt angle is listed. Each DMD data sheet specifies the actual tilt angle and how
much it can vary.
Fill factor - The mirror array constitutes discrete micro-mirrors with a given mirror pitch. Fill factor is definedas the percentage of light reflected by the on-state mirrors when illuminated by a beam of light incident at
2x the mirror tilt angle with the assumption of 100% mirror reflectivity. For the actual mirror reflectivity, see
Section 5. The mirror pitch, structure and tilt angle are directly related to the fill factor value. Geometrical ray
trace simulation methods are used to calculate fill factor for DMD arrays.

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Window Properties

Table 2-1. DMD On-State Fill Factor

(1)
(2)
(3)

DMD Examples (1)MICROMIRROR
Pitch (µm)

Nominal Tilt Angle(deg.)

Illumination
f-number

Typical On-State Fill
Factor (2) (3)

DLP7000

13.68

12

2.4

92%

DLP650LE

10.8

12

2.4

92%

DLP780TE
DLP800RE

9.0

14.5

2.0

97%

DLP3030-Q1
DLP5534-Q1
DLP4501
DLP9000

7.6
7.6
7.56
7.56

12

2.4

94%

DLP3010

5.4

17

1.7

93%

DMD example list is not comprehensive and many other devices may be available within each micromirror pitch category.
On state fill factor values are approximate. Refer to DMD data sheet for device-specific values.
The on state fill factors are calculated using illumination at the native f-number corresponding to the tilt nominal angle.
a.
b.
c.

12° tilt = f/2.4
14.5° tilt = f/2.0
17° tilt = f/1.7

3 Window Properties
The two main types of DMD windows are directly related to the packaging types:••

Type A DMD packaging uses Corning 7056 glass (typically about 3 mm thick).
Wafer Level Packaging (WLP, often referred to as Sxxx package) uses Corning Eagle XG glass (typically
about 1 mm thick or less).

Both the WLP window and the Type A window have an anti-reflective thin film coating to reduce reflections andincrease transmission efficiency. Depending on the application, either the visible, UV, or NIR coating is used.
The values below describe a single pass of visible light (420 nm–680 nm) with random polarization throughthe window, and accounting for two surface coatings.
••

Average transmittance, Tave ≥ 99% at all angles 0–30° AOI,
Average transmittance, Tave ≥ 97% at all angles 30–45° AOIAll transmittance values are the total transmittance of the window (through both surfaces and glass). A
transmission number of 96% is used in the Table 6-1 calculation representing a double pass through the window
with approximately 99% transmission at each coated surface. See the DMD data sheets for device specificvalues.
For more information on window transmittance, see Wavelength Transmittance Considerations for DLP® DMD
Window.

4 Mirror Diffraction Efficiency
4.1 Mirror Flatness
The semiconductor processing required to build the mirror structure can result in the mirrors deviating froma perfectly flat plane. However, the processing is designed and controlled to minimize the non-flatness or
non-planarity of the mirror. Diffraction modeling described below can be used to predict losses due to non-flat
mirrors. However, the calculation below assume a flat mirror.

4.2 Mirror Diffraction Efficiency
The active array area consists of a large rectangular array of aluminum-based mirrors which can tilt to one oftwo stable angles. For the 13.68 μm, 10.8 μm, and 7.6/7.56 μm micromirror pixel sizes, this is typically +12° and–12° around the diagonal. The 9.0 μm micromirror pixel size also tilts around the diagonal at typically +14.5°
and –14.5°. The 5.4 µm micromirror pixels are different in that they tilt approximately 17° about the orthogonal
direction.

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The illumination and projection f-numbers are typically matched to obtain the tradeoff of efficiency and contrast
ratio. However, even under these conditions, there is some loss of light due to clipping of the diffracted light at
the projection lens aperture stop. Because the size of the mirrors is not large with respect to the wavelength, themirror reflected light diffracts into a larger cone angle which results in a loss of light.
The longer wavelengths (red) are diffracted more than shorter wavelengths (blue), resulting in diffraction
efficiency that typically decreases at longer wavelengths.
In order to more accurately model the complex diffraction pattern that arises, use the fact that the array of tilted
mirrors behaves similarly to a classic blazed optical diffraction grating. Conceptually, the best way to approach
broadband source diffraction is to consider it as a combination of a large number of plane waves varying inwavelength and direction. All of these plane wave sources can be combined incoherently to assess the final
diffraction pattern.
For a two-dimensional array of mirrors illuminated by a single wavelength, collimated laser beam, the far fieldappears as an array of bright points (diffraction orders) that are spaced approximately by λ/pitch in angle, where
λ is the wavelength. Scalar diffraction theory that can be approximated using the fast Fourier transform algorithm(FFT) can generally be used for this calculation with reasonably good accuracy. The amplitude of the array ofbright points is modulated by the far-field pattern of an individual mirror which is generally close to a sin(x)/x
shape. The far-field radiance function can be calculated as a function of direction cosines α and β using theFourier transform as described in Equation 2.

(2)Here, the quantity

represents the EM field (magnitude and phase) as it leaves the surface of

the DMD mirror array. The calculated radiance profile,, can then be mathematically truncatedcorresponding to the acceptance angle defined by the projection lens aperture. By integrating the radiance overincident angle and wavelength and keeping track of the power inside the aperture relative to the total power, you
can calculate the diffraction efficiency.
The resulting far-field radiance pattern for a white-light incoherent source has radiating arms of alternating color
as shown in Figure 4-1. The energy in the outer arms is lost as only the central part of the beam is collected by
the projection lens. The calculated diffraction efficiency varies with mirror pitch, mirror tilt, and wavelength.
Because the far-field diffraction pattern (or image at the projection pupil) depends upon illumination angle,
mirror pitch, mirror tilt angle, and wavelength, the far-field diffraction from white light has a significant amountof color variation. The most important factors in determining diffraction-induced color variation are mirror pitch
and mirror tilt angle, the illumination angle being less of a factor. This color variation causes the diffraction
efficiency to vary approximately as a sinusoid as a function of wavelength as shown in Figure 4-3 through Figure
4-7. A spectral plot of diffraction efficiency shows periodic oscillations in wavelength, and the period of thoseoscillations generally depends on the pitch of the mirrors—the smaller pitch mirrors showing a longer period. As
a result, the diffraction efficiency can change significantly as a function of wavelength. Also, variation in tilt angle
across the DMD mirror array and from device to device causes the spectral peaks to shift in wavelength.

4

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Mirror Diffraction Efficiency

Figure 4-2 shows the calculated nominal diffraction efficiency for the various pixel types as a function of pixel
pitch. As expected, there is a general reduction in diffraction efficiency as the pixel is scaled down in pitch.

Diffracted
light

Projection aperture

Figure 4-1. Simulated 5.4 µm Pitch DMD Far Field Radiance Image; Dashed Circle Shows Outline ofProjection Lens Aperture Edge

Figure 4-2. Summary of Calculated Average Photopic Diffraction Efficiencies for Different Pixel Sizes(420 nm–680 nm wavelength)

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Figure 4-3 through Figure 4-7 show the spectral diffraction efficiencies for different f-numbers matched between
illumination and projection, and nominal design tilt angles.
1.00
0.95

Diffraction Efficiency

0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
400

f/2.4, 24 Illumination
f/3.0, 24 Illumination
450

500

550

600

650

700

Wavelength (nm)Figure 4-3. 13.68 µm Pitch DMD Mirror Calculated Diffraction Efficiency (matched illumination andprojection f-numbers)
1.00
0.95

Diffraction Efficiency

0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
400

f/2.4, 24 illumination
f/3.0, 24 illumination
450

500

550

600

650

700

Wavelength (nm)Figure 4-4. 10.8 µm Pitch DMD Mirror Calculated Diffraction Efficiency (matched illumination andprojection f-numbers)

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Mirror Diffraction Efficiency
1.00
0.95

Diffraction Efficiency

0.90
0.85
0.80
0.75
0.70
0.65
0.60
f/2.0, 29 illumination
f/2.4, 29 illumination
f/3.0, 29 illumination

0.55
0.50
400

450

500

550

600

650

700

Wavelength (nm)Figure 4-5. 9.0 µm Pitch DMD Mirror Calculated Diffraction Efficiency (matched illumination andprojection f-numbers)
1.00
0.95

Diffraction Efficiency

0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
400

f/2.4, 24 illumination
f/3.0, 24 illumination
450

500

550

600

650

700

Wavelength (nm)Figure 4-6. 7.56 µm Pitch DMD Mirror Calculated Diffraction Efficiency (matched illumination andprojection f-numbers)

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1.00
0.95

Diffraction Efficiency

0.90
0.85
0.80
0.75
0.70
0.65
0.60
f/1.7, 34 illumination
f/2.4, 34 illumination
f/3.0, 34 illumination

0.55
0.50
400

450

500

550

600

650

700

Wavelength (nm)Figure 4-7. 5.4 µm Pitch DMD Mirror Calculated Diffraction Efficiency (matched illumination andprojection f-numbers)

4.3 Diffraction Efficiency with Mismatched Illumination and Projection f-numbers
The mismatched f-number approach is a method to improve diffraction efficiency performance. By utilizing aslower illumination f-number (larger f-number) and faster projection f-number (smaller f-number), the diffraction
efficiency increases because more of the diffracted light from the reflected illumination beam is collected into theprojection lens aperture. An example case is a system with the 7.56 μm pitch DMD, f/3 illumination and f/2.4
projection optics as shown in Figure 4-8. The matched f/2.4 illumination and f/2.4 projection case has an averagediffraction efficiency of 83.9% while the mismatched f/3 illumination and f/2.4 projection case has an averagediffraction efficiency of 90.5%. This method works across DMD devices. The margin of improvement depends
largely on the selected f-numbers and DMD mirror size being used.
1.00
0.95

Diffraction Efficiency

0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
400

f/2.4/2.4 Matched
f/3.0/2.4 Mismatched
450

500

550

600

650

700

Wavelength (nm)Figure 4-8. 7.56 μm Pitch DMD Mirror Calculated Diffraction Efficiency With Matched and Mismatchedf-numbers

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Mirror Reflectivity

A direct laser system, where larger illumination f-numbers (smaller illumination system etendue) does not
significantly lower the projector luminous output, benefits from the mismatched f-number technique. In a slower
f-number system with matched illumination and projection f-number, the local minima for a given diffraction
efficiency curve is lower as compared to a faster, matched f-number system. This reduced diffraction efficiency
can be greatly improved by utilizing the mismatched f-number technique, driving the diffraction efficiency muchhigher than a matched f-number system would provide. The mismatching of f-number in this way flattens or
reduce the peak to valley difference in the diffraction efficiency curves.
The mismatched f-number technique trades off some system contrast for diffraction efficiency. The system
contrast lies between the lower matched f-number and the higher matched f-number of those of the projection
and illumination path. For example, for a mismatched f-number system in which the illumination is f/3 andprojection is f/2.4, the contrast is higher than a f/2.4 matched projection system and lower than a f/3 matchedprojection system built around the same DMD.

5 Mirror Reflectivity
The active array area consists of a large rectangular array of aluminum based mirrors. The mirrors are nominally89% reflective in the visible range (420 to 680 nm).
1.00
0.98

Mirror Reflectivity

0.96
0.94
0.92
0.90
0.88
0.86
0.84
0.82
0.80
400

450

500

550

600

650

700

Wavelength (nm)Figure 5-1. DMD Mirror Typical Reflectivity

6 Estimating Overall DMD Efficiency
Overall optical efficiency can be estimated using Equation 3.
EfficiencyDMD = transmissionwindow × efficiencyfillfactor × efficiencydiffraction × reflectivitymirror × transmissionwindow

(3)

where
•
•
•
•

efficiencyfillfactor is the fractional mirror coverage (on-state mirrors) as viewed from the illumination direction
transmissionwindow is single-pass window transmission including two anti-reflection surfaces. This term is
accounted for twice because light travels through the window twice.
efficiencydiffraction is the mirror array diffraction efficiency which can include effects of non-flat mirrors
reflectivitymirror is the mirror reflectivity including mirror scatter

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References

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The photopic numbers shown in Table 6-1 assume a source with a flat power spectrum with wavelengths of 420
nm–680 nm. More accurate results can be obtained for a given light source by multiplying the spectral diffraction
efficiency by the actual source spectrum.
Table 6-1. Total Photopic Average Efficiency Calculation(1)On-State Fill

Window
Transmission(Double Pass)

Mirror Refl.

Total Eff.

92%

96%

89%

70%

87%

92%

96%

89%

68%

89%

97%

96%

89%

72%

2.4

84%

94%

96%

89%

67%

17

1.7

86%

93%

96%

89%

68%

17

2.4

80%

93%

96%

89%

64%

DMD Pitch (μm)

Tilt Angle(deg)f-numberDiff. Eff.

13.68

12

2.4

89%

10.8

12

2.4

9.0

14.5

2.0

7.6/7.56

12

5.4
5.4
(1)

The values in this table are approximate. For specific values, see the device-specific DMD data sheet.

7 References•“Linear systems formulation of non-paraxial scalar diffraction theory” James E. Harvey, Proc. of SPIE Vol.
8122

8 Revision History
NOTE: Page numbers for previous revisions may differ from page numbers in the current version.
Changes from Revision A (June 2019) to Revision B (April 2023)
Page• Updated the numbering format for tables, figures and cross-references throughout the document.................. 2• Updated Table 2-1 ............................................................................................................................................. 2• Updated Section 3 ............................................................................................................................................. 3• Updated Section 4.1 .......................................................................................................................................... 3• Added 9.0 μm pixel and update figures in Section 4.2 ...................................................................................... 3• Added Section 4.3 ............................................................................................................................................. 8• Added Figure 5-1 ...............................................................................................................................................9• Updated Table 6-1.............................................................................................................................................. 910

DMD Optical Efficiency for Visible Wavelengths

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