(12) United States Patent
`Rancuret et al.
`
`(10) Patent N0.:
`(45) Date 0f Patent:
`
`US 6,958,841 B2
`Oct. 25, 2005
`
`US006958841B2
`
`(54) GENERATION OF DIGITAL PATTERNS FOR
`SPATIAL LIGHT MODULATION
`
`(58) Field of Search ............................... .. 359/238, 290,
`359/291, 292
`
`(75) Inventors: Paul L. Rancuret, Plano, TX (US);
`Terry A. Barlett, Dallas, TX (US);
`Benjamin L. Lee, Duncanville, TX
`(US); Elisabeth Marley Koontz,
`Dallas, TX (US)
`
`t d
`t I
`I t
`: T
`73 As '
`(
`)
`slgnee Diggss, gigzlélgn S ncorpora e ’
`
`( * ) Notice:
`
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`U.S.C. 154(b) by 617 days.
`
`(21) APPL NO; 10/154,257
`_
`(22) Flled:
`(65)
`
`May 23! 2002
`Prior Publication Data
`
`US 2003/0001953 A1 Jan. 2, 2003
`_
`_
`_ Related U-_S- Apphcatlon Data
`_
`(60) PTOVlSlOnaT apphcatlon NO- 60/293426: ?led on May 23:
`2001'
`(51) Int. Cl.7 .......................... .. G02B 26/00; G02F 1/01
`(52) US. Cl. ...................... .. 359/239; 359/291; 359/292
`
`(56)
`
`References Cited
`
`U-S- PATENT DOCUMENTS
`6,055,086 A
`4/2000 Soutar et 211.
`2002/0079432 A1
`6/2002 Lee et a1.
`2002/0081070 A1
`6/2002 TeW
`'
`Primary Examiner—David Spector
`(74) Attorney, Agent, or Fzrm—Charles A. Brill; Wade
`James Brady’ HI; Fredenck J‘ Telecky> Jr‘
`(57)
`ABSTRACT
`
`Disclosed is a method for generating patterns to be used in
`a spatial light modulator having a plurality of pixels. The
`method includes generating an optical pattern to be placed
`upon the pixels of the spatial light modulator, applying the
`optical pattern to 'the pixels of the spatial light~ modulator,
`measurmg the optical performance of the plurality of pixels
`having the optical pattern applied to it, comparing the
`measured optical performance to a target optical
`performance, and adjusting the optical pattern applied to the
`plurality of pixels to form another optical pattern that more
`closely achieves the target optical performance.
`
`39 Claims, 13 Drawing Sheets
`
`T202\
`
`—T 2
`
`“P
`PATTERN
`PROCESSING
`
`VALUES
`
`LOOK-UP
`T1285;
`PATTERN
`PATTERN’ —
`
`____ _ _
`
`/
`
`I
`
`SENSOR
`
`1210
`
`1 16 1204 PATTERN
`‘
`DMD
`
`:
`|
`|
`_PNlEBN____ 5
`
`11
`0
`
`FNC 1010
`
`

`

`U.S. Patent
`US. Patent
`
`Oct. 25,2005
`Oct. 25, 2005
`
`Sheet 1 0f 13
`Sheet 1 0f 13
`
`US 6,958,841 B2
`US 6,958,841 B2
`
`110
`
`103
`
`102
`
`106
`
`

`

`US. Patent
`
`Oct. 25, 2005
`
`Sheet 2 0f 13
`
`US 6,958,841 B2
`
`114
`
`204
`
`204
`
`204
`
`204
`
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`CZECCCDCDEGDUDDD20303303333223
`33323330ODDUUCCGJZDUDUUDDDDDCU
`0—1.ECUDD::CCESSUTZ23.2.333330020
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`:3SUCDUDDCCUDBDCDCQCCDDDUDEE:
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`
`FIG.
`
`2
`
`204b
`
`210
`
`2040
`
`204C
`
`FIG.
`
`2A
`
`

`

`U.S. Patent
`
`Oct. 25,2005
`
`Sheet 3 0f 13
`
`US 6,958,841 B2
`
`DISPERSION
`
`DISPERSION
`
`FIG. 3B
`
`

`

`U.S. Patent
`
`Oct. 25,2005
`
`Sheet 4 0f 13
`
`US 6,958,841 B2
`
`FIG. 3C
`
`5
`
`5
`
`4
`3 NON-INTERLACED
`PIXELS
`
`FIG. 48
`
`Q
`
`Q
`@412
`@ é
`\
`
`

`

`U.S. Patent
`
`Oct. 25,2005
`
`Sheet 5 0f 13
`
`US 6,958,841 B2
`
`502
`
`FIG. 5
`
`502
`
`FIG. 8A
`
`

`

`US. Patent
`U.S. Patent
`
`Oct. 25,2005
`Oct. 25, 2005
`
`Sheet 6 0f 13
`Sheet 6 0f 13
`
`US 6,958,841 B2
`US 6,958,841 B2
`
`
`
`

`

`U.S. Patent
`US. Patent
`
`Oct. 25,2005
`Oct. 25, 2005
`
`Sheet 7 0f 13
`Sheet 7 0f 13
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`US 6,958,841 B2
`US 6,958,841 B2
`
`
`
`

`

`US. Patent
`
`Oct. 25, 2005
`
`Sheet 8 0f 13
`
`US 6,958,841 B2
`
`_p_.
`
`(N
`
`
`
`to(14 w_.
`
`
`
`
`
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`
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`
`
`
`
`FIG. BB
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`
`
`
`
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`
`
`
`
`
`
`------------
`-----—-----------
`Immun-
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`
`
`
`
`FIG. 72
`
`
`
`PATTERN
` 120
`PROCESSING
`
`
`LOOK-UP
`VALUES
`
`PATTERN
`,
`
`PATTERN
`
`
`
`LOOK-UP
`TABLE
`
`
`
`
`SENSOR
`
`
`
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`
`fl
`
`E I
`
`II
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`
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`
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`
`

`

`U.S. Patent
`
`Oct. 25,2005
`
`Sheet 9 0f 13
`
`US 6,958,841 B2
`
`FIG. 8D
`
`OR
`
`FIG. 8E
`
`

`

`U.S. Patent
`
`Oct. 25,2005
`
`Sheet 10 0f 13
`
`US 6,958,841 B2
`
`FIG. 8F
`
`0R
`
`FIG. 8C
`
`

`

`U.S. Patent
`
`Oct. 25,2005
`
`Sheet 11 0f 13
`
`US 6,958,841 B2
`
`FIG. 8H
`
`OR
`
`FIG. 8!
`
`

`

`US. Patent
`
`Oct. 25, 2005
`
`Sheet 12 0f 13
`
`US 6,958,841 B2
`
`906
`
`
`
`
`ATTENUATION
`
`COMMANDS (A) 11 _N
`
`
`
`913
`
`1002
`
`INCREASE ATTEN
`
`DECREASE ATTEN
`
`
`
`(PIXELS OFF)- (PIXELS ON)
`
`
`
`
` X'=[X+De|lo_
`Phosor(S(k))] 2
`
`

`

`U.S. Patent
`
`Oct. 25,2005
`
`Sheet 13 0f 13
`
`US 6,958,841 B2
`
`FIG. 17
`—I
`1102
`GENERATE PERIODIC
`PATTERN (0-,) f
`I
`MEASURE/RECORD [1 104
`b] =xx.xx dB
`
`1:
`
`IS WITHIN A 0F
`
`ATIENk?
`
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`
`AttenPotternk
`NULL?
`
`IS b-
`CLOSER To‘ Atten
`THAN b]?
`
`k
`
`NO
`
`NEXT PATTERN
`OR DONE
`SET k=1
`I
`FINE TUNING
`ALGORITHM
`
`\
`1 I20
`
`\1 122
`
`111O
`/
`ASSIGN AttenPottern k =0 ;
`
`1114
`/
`REPLACE 0]- WITH 0;
`IN AttenPotterm<
`
`1118
`/
`CHOOSE 0; OR 0] RANOOMLY
`TO PUT INTO AttenPotiernk
`
`>
`
`w
`
`11
`
`

`

`US 6,958,841 B2
`
`1
`GENERATION OF DIGITAL PATTERNS FOR
`SPATIAL LIGHT MODULATION
`
`RELATED APPLICATIONS
`
`This application depends from and claims priority to US.
`Provisional Patent Application No. 60/293,126, ?led May
`23, 2001, Which is hereby incorporated by reference herein.
`
`REFERENCE TO APPENDIX
`
`Attached to this application is Appendix I, Which is an
`exemplary compilation of patterns for an embodiment of a
`spatial light modulator.
`
`TECHNICAL FIELD
`
`Described in this application are patterns and methods for
`generating patterns for the modulation of optical signals
`using a pixel-based spatial light modulator.
`
`BACKGROUND
`
`A pixel-based Spatial Light Modulator (“SLM”) can be
`used to modulate an incoming light signal. SLMs can be
`used in many contexts, such as in projection displays,
`printing, telecommunications, and in other types of light
`processing. In a telecommunications context, an incoming
`light signal can have multiple different channels or carrier
`Wavelengths. In these contexts, differing patterns of pixels
`are used to achieve differing desired performance charac
`teristics of the modulated light signal. A challenge, hoWever,
`is to determine the pixel patterns, from all the possible pixel
`patterns, to be used to achieve the desired optical perfor
`mance characteristics.
`
`SUMMARY
`
`This application describes embodiments for determining
`pixel patterns to be used or applied in a pixel-based SLM to
`achieve certain optical response characteristics. This appli
`cation further describes embodiments for tuning the optical
`response characteristics of SLMs and sub-arrays of pixels in
`SLMs. One optical response being characteriZed in the
`embodiments described in this application is that of optical
`attenuation, but other optical response characteristics also
`may be accommodated. For example, pixel patterns could
`also be chosen for their phase effects on the incoming optical
`signal or on the patterns’ abilities to spatially separate or
`sWitch incoming optical signals.
`In one approach, the optical response of each individual
`pixel Within certain segments of the SLM is determined.
`Using that information, it can be determined Which pixels
`can be added together to generate a desired composite
`response to an incoming light signal. The SLM may contain
`a number of segments or sub-arrays Which can be assigned
`to certain channels or Wavelengths (or ranges of channels or
`Wavelengths) of an incoming light signal having multiple
`such channels or Wavelengths, and these segments can all be
`characteriZed such that appropriate patterns for each seg
`ment can be determined.
`In determining patterns to be used to modulate the sepa
`rate channels or Wavelengths of an incoming light signal by
`segments of the SLM, the patterns may be distinct, aperiodic
`patterns, or patterns may be periodic patterns to be applied
`across some or all of segments (or parts of the segments). In
`either case, the optical response of the segments having
`these patterns can be tuned by turning on or off certain
`pixels. Predetermined or calculated sequences can be pro
`
`10
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`15
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`20
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`25
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`2
`vided for the toggling of these pixels, making use of the fact
`that certain pixels Within a segment may be knoWn to have
`a larger or more coarse in?uence on modulated, light signals,
`Whereas others Will have a smaller or ?ner response on the
`light signals. Knowledge of the characteristics of the pixels
`and/or periodic pixel patterns Will enable generation of
`segment pixel patterns Without applying a “brute force”
`method of trying every single pattern Within a segment in
`order to ?nd certain optical response characteristics. In other
`Words, it is possible to reduce the analysis for determining
`light patterns to a smaller subset of patterns out of all
`possible patterns Within a segment.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`FIG. 1 is a perspective vieW of an optical system into
`Which a SLM can be placed;
`FIG. 2 is a top vieW of an SLM onto Which several
`channels of an optical signal have been spread out for
`modulation;
`FIG. 2A is a top vieW of three segments of an SLM such
`as described in FIG. 2, but in Which a channel of the optical
`signal is distributed across several segments;
`FIGS. 3A—B shoW a periodic pattern applied to an SLM.
`FIG. 3C and the referenced Appendix I shoW a pixel
`segment con?guration and a group of non-periodic pixel
`patterns that can be applied to it to achieve desired optical
`performance characteristics;
`FIGS. 4A—4B are top vieWs of a traditional aperture and
`a digital, pixelated aperture;
`FIG. 5 is an exemplary superposition of a Gaussian spot
`distribution relative to a segment of pixels on an SLM;
`FIGS. 6A—6B are phasor model predictions for the optical
`response due to each “on” pixel (for 6A) and each “off” pixel
`(for 6B) in a segment of an SLM;
`FIG. 7 is an exemplary mapping of vectors on a phasor
`coordinate system;
`FIGS. 8A—8I are pixel sequence map schemes that can be
`used for the ?ne-tuning of optical responses of a segment of
`an SLM;
`FIG. 9 is a ?oWchart of a method for calibrating a segment
`or segments of an SLM;
`FIG. 10 is a ?oWchart of a ?ne-tuning method for patterns
`applied to an SLM;
`FIG. 11 is a ?oWchart of a method by Which patterns can
`be initially generated and associated With certain desired
`optical response characteristics; and
`FIG. 12 is a block diagram of a system for carrying out the
`methods for generating optical patterns.
`All of these draWings are draWings of certain embodi
`ments. The scope of the claims is not to be limited to the
`speci?c embodiments illustrated in the draWings and
`described beloW.
`
`DESCRIPTION OF THE EMBODIMENTS
`
`FIG. 1 is a perspective vieW of the components of an
`optical signal processing system in Which the embodiments
`described in this patent application can be used. ShoWn in
`FIG. 1 is an input light collimator 102, Which receives an
`optical light signal input on optical ?ber 103. From the input
`102, a free-space optical signal enters the system 104. The
`optical signal 104 can have from 1 to N channels, each of
`Which may be a separate Wavelength “7t” (K1, K2 .
`.
`. 7t”).
`Free-space optical signal 104 is directed toWards a grating
`106, Which Will spatially separate the optical channels
`
`

`

`US 6,958,841 B2
`
`10
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`15
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`25
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`35
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`3
`slightly so that they Will travel along slightly diverging
`optical paths. These diverging optical paths then pass
`through an imaging lens 108, Which purpose is to focus the
`optical signals on to the DMD.
`The path betWeen the lens 108 and the DMD 114 may
`contain a mirror 110 for re?ecting the signal back generally
`toWards the direction from Which it came. Provided next to
`the DMD is a correction lens 111, Which can be used to
`adjust for situations Where the grating is not at the ?rst focal
`point of the imaging lens 108. In other Words, the correction
`lens alloWs the path length from the grating 106 to the
`imaging lens 108 to be different from the focal length of the
`lens 108. Folding mirror 112 is provided to direct the light
`signals onto the DMD 114. Because of the separation of
`channels provided by the grating 106, each channel Will fall
`on a slightly different portion of the DMD surface. The
`DMD 114 Will re?ect the light beam back toWards the mirror
`112, but the mirrors of the DMD 114 Will modulate the
`incoming light signal such that the DMD acts as an optical
`signal processor. This optical signal processing could be, for
`example, optical attenuation, Wavelength ?ltering, optical
`performance monitoring, co-channel modulation, or disper
`sion compensation. In systems employing multiple ports, the
`optical signal processor can be employed as an add/drop
`multiplexer. Another purpose for the optical signal process
`ing performed by the DMD 114 could be to provide a
`programmable optical source, such can be formed from a
`Wide-band optical laser Whose input is ?ltered doWn to make
`it appear as if it Were one or more sources of narroW-band
`light.
`Still referring to FIG. 1, after re?ection from the DMD
`surface and the mirror 112, the light signals return along a
`return path 116 through mirror 110 and imaging lens 108.
`Although this path is similar to the path for the incoming
`light beam 104, it is slightly spatially separated, such that
`When the beam strikes the grating 106 again on the return
`path, it is spatially offset from the position Where it struck
`the grating 106 as the incoming path 104. The optical grating
`106 thereupon re-converges the multiple channels, and
`directs them toWards a mirror 115, Which is also separated
`from the incoming beam 104, but is in line With the return
`beam 116 as shoWn in the FIG. 1. From the mirror 115, the
`re?ected light beam 116 is directed toWards an output of the
`system, Which is preferably also a collimator 120.
`The structure of the optical system of FIG. 1 is just an
`example of an optical system in Which the embodiments
`discussed in this application can be applied. For example, in
`the application shoWn in the ?gure, the incoming light signal
`is re?ected from the DMD in a manner such that the
`re?ected light signal does not travel along the same path as
`the incoming light signal. In some applications, it may be
`desirable to direct the re?ected beam back along the same
`path and use a circulator to separate the incoming and
`outgoing beam.
`FIG. 2 is a top vieW of the DMD 114. ShoWn on FIG. 2
`and on the surface of the DMD 114 are a plurality of
`individual pixel elements 202. These individual pixel ele
`ments are, in one embodiment, individual DMD mirrors,
`Which can be individually sWitched on and off by circuitry
`underlying the DMD pixels on a semiconductor substrate. In
`such an embodiment, the array may be a 768><l024 array,
`although many other array dimensions could be used.
`Besides DMD-type spatial light modulators, the principles
`employed here could also be applied to liquid crystal dis
`plays or other types of spatial light modulators.
`Also shoWn on the surface of the DMD 114 are a number
`of segments or sub-arrays 204 of pixels. The segments
`
`40
`
`45
`
`55
`
`65
`
`4
`represent divisions of the area in Which the multiple chan
`nels of the incoming free-space optical signal 104 can strike
`the surface of the DMD 114. In this description of the
`embodiments, the area in Which the plurality of channels of
`the optical signal strike the DMD Will be referred to as the
`band 206, Whereas the sub-arrays in Which the channels
`strike are referred to as segments 204. Thus, as shoWn here,
`there Would be a segment 204 devoted to receiving a ?rst
`channel, A1, a second channel A2, a third channel k3, and so
`on, up until an nth channel 7t”. Within each segment 204, in
`general the intensity distribution Will be Gaussian in shape
`due to the mode of the single-mode ?ber. Although FIG. 2
`shoWs each individual channel as being contained Within a
`single band 206, and striking Within a single segment 204,
`it is also possible to have the 1/e2 area, Which is the area
`containing 91% of the poWer, of the incoming channel signal
`210 striking over multiple segments 204a—c, as shoWn in
`FIG. 2A. This ?exibility is made possible because this is an
`optical signal processing application, and therefore the sys
`tem can be programmed to handle the division of optical
`Wavelengths among one or multiple segments 204. For
`example, FIG. 2A shoWs an application in Which the 1/e2
`distribution of the particular Wavelength channel 210 of the
`optical signal 104 is distributed across three segments, 204a,
`204b, and 204c. Rather than distributing the channel 210
`over three segments, the channel signal 210 applied onto a
`signal segment 204, or onto tWo, three, four or any other
`number of segments, according to the Way in Which the
`system is programmed to process the incoming optical light
`signals.
`Once the different optical channels have been distributed
`across the multiple segments 204 of the band 206, signal
`processing is applied to operate the spatial light modulator
`elements controlling those different segments 204. One
`challenge is determining Which pixels to turn on or off to
`achieve the signal processing results that are desired. Since
`a given segment 204 may have any number of pixels, and
`since the number of combinations of different pixels rises
`exponentially as the number of elements increases, a brute
`force method for determining the different arrays of the
`pixels elements can quickly overWhelm a system for deter
`mining the patterns to be used to achieve the signal pro
`cessing results. Described in this application is a system and
`method for more ef?ciently determining patterns to be
`applied to the pixels of the different segments 204 in order
`to achieve the goals for signal processing.
`FIG. 3A illustrates an embodiment in Which a periodic
`pattern 301 is applied across the segment 304 in order to
`provide the desired optical signal processing. For example,
`a certain periodic pattern 301 can be applied across a 2x3
`subset of pixel pairs or base units 302 Within the segment
`304, and this pattern 301 can be repeated for each 2x3 group
`of pixel pairs 302 across the segment 204. For example,
`Within a 12x12 array of pixels, limiting the periodicity to
`2x3 pixel-pair patterns Will result in approximately 4500
`unique periodic patterns needing to be generated and applied
`to the segment 304. Thus, rather than the 1043 of unique
`patterns that may be found in a complete 12x12 pattern, by
`using the periodicity, the number of unique patterns Which
`must be generated is greatly reduced. The process of gen
`erating the patterns to be applied to achieve the signal
`processing objectives is therefore greatly simpli?ed.
`FIG. 3B shoWs an exemplary pattern 301 that may be
`applied and repeated through out the segments 304, such as
`to the segment 304 shoWn in FIG. 3A. In this example, the
`“on” pixels 306 are shoWn by the light-colored pixels,
`Whereas the “off” pixels 308 are darkly shaded. A number of
`
`

`

`US 6,958,841 B2
`
`5
`different patterns can be applied and repeated across the
`segments 304 in order to achieve different optical perfor
`mance characteristics. These base units Were chosen, in part,
`so that the tWo directions of periodicity Would be orthogonal
`and parallel respectively to the dispersion direction across
`the DMD. The simplest base unit is a single pixel With an
`“on” and “off” state.
`Within FIG. 3B there are shoWn six base units 302
`arranged in a 2x3 grouping 304. While the base units 302 are
`shoWn having tWo pixels 202 each, it Would also be possible
`to have base units of one, three, four, ?ve, or other multiples.
`Any n><m set of pixels, Where n and m are positive integers,
`can be chosen as a base unit. Further, it is possible for the
`group 304 to be comprised of tWo, three, four, ?ve or any
`other number of base units 302. Again, any n><m set of base
`units, Where n and m are positive integers, can be chosen as
`group or “tile.” So that the optical performance is reasonably
`insensitive to alignment, the tile siZe is designed in these
`embodiments to be much smaller in both orthogonal direc
`tions than the spot siZe. As an example, the tile siZe may be
`designed to be approximately 20% or less of the spot Width
`in the corresponding dimensions.
`FIG. 3C provides an example of a segment 204 in Which
`a non-periodic set of pixel patterns is applied to modulate the
`incoming light signal. In this example, there are provided 7
`columns and nineteen roWs, and in Which the roWs alternate
`betWeen 6 and 7 pixels each. In other Words, roW 1 has 7
`pixels, roW 2 has 6 pixels placed above and betWeen
`adjacent pixels of the ?rst roW, roW 3 has 7 pixels above and
`spaced on either side of the pixels of roW 2, and so on. This
`arrangement of pixels for the segment 204 shoWn in FIG. 3C
`is merely exemplary. Other arrangements of pixels having
`different numbers of roWs or different numbers of columns
`could be used, and is further possible to have an arrangement
`of pixels in Which each roW Would have the same number of
`pixels. Provided in Appendix I are a set of aperiodic patterns
`that has been adapted to this group of pixels and Which are
`designed to provide a range of desired optical responses.
`This is an example of the adaptation of pixel patterns to
`effect desired optical performance characteristics, and many
`patterns could be applied to many SLM pixel arrays or
`sub-arrays in accordance With the methods and systems
`described in this application. Further, the effects of both
`periodic and non-period pixel patterns can be combined in a
`given pixel pattern. A periodic pixel pattern can be given
`non-periodic variations interspersed Within it to tune the
`optical performance characteristics. Alternatively, there can
`be certain areas Within a pixel pattern that have periodically
`repeating patterns and other certain areas Within a pixel
`pattern that have non-periodic patterns. These combination
`periodic/non-periodic pixel patterns can be de?ned as start
`ing pixel patterns, or they can be generated as a part of the
`pixel pattern ?ne-tuning process described in this applica
`tion.
`Whether periodic or non-periodic pixel patterns are used
`Within the segments 204 Will depend on the performance
`characteristics and advantages hoped to achieve through the
`particular pattern selected. Non-periodic (spot-related) pat
`terns sloWly diffuse energy in to the Fraunhover envelope
`halo that results from the ?nite extent of the aperture.
`Periodic patterns instead make more orders available to
`alloW energy to be diverted. If the pattern period is reason
`ably small compared to the siZe of the 1/e2 spot, then the
`approximate attenuation level becomes less sensitive to
`alignment. Currently, that means restricting the period to
`about 2 pixels in any direction. This is based on the current
`optical design of the beam spot area that is directed on to a
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`given segment 204, and on current process technology.
`Thus, through advances in process technology and system
`design, it may be possible to have a periodic pattern of
`greater than tWo.
`Above, the term “aperture” Was used. A traditional “aper
`ture” blocks energy equally from about the perimeter of an
`opening, Whereas the digital aperture referred to herein, due
`to its digital nature, alloWs for the possibility of picking the
`points Within the opening at Which energy becomes blocked.
`In other Words, in a traditional circular aperture to reduce the
`siZe of the aperture requires a gradual reduction of the
`opening about the entire circumference. In a digital aperture,
`hoWever, such as provided by the pixels shoWn in FIGS. 3A,
`3B, and 3C, it is possible to selectively remove individual
`mirrors from those that are providing the transmitted or
`re?ected light, thereby providing greater ?exibility in hoW
`the aperture is de?ned.
`The concept of a traditional vs. a digital aperture is
`illustrated in FIGS. 4A—B. FIG. 4A, for example, shoWs a
`traditional aperture 400, Which de?nes an opening 402 that
`can be adjusted as shoWn by the arroWs 404. In other Words,
`the opening 402 is set to be closer or farther from the outer
`circumference. In this Way, the opening 402 is adjusted to
`alloW more or less light to pass through it. Conversely in
`FIG. 4B, Which is an array of 410 pixels, individual pixels
`Within the array 410 can-be turned “off” selectively to
`reduce the amount of light being re?ected from the array of
`410. This turning off of the pixels at locations throughout the
`array alloWs more ?exibility in hoW much light may pass
`through, thereby alloWing “off” pixels 412 to be turned
`“off”, not only for the effect on the amplitude of the re?ected
`signal, for example, but also for the secondary effects
`imparted on the signal by the turning off of the particular
`pixel 412. Secondary effects that can be tailored by this
`technique include the de?nition of phase effects upon the
`composite re?ected light signal.
`FIG. 5 provides an array of pixels such as Would be used
`in a segment 204, and it shoWs Gaussian light distributions
`superimposed relative to the array of pixels onto Which the
`light is illuminated or applied. This Gaussian distribution
`502 Would generally be an elliptical area of light intensity,
`centered someWhere near the middle of the segment 204. For
`example, in a rectangular array of pixels comprising the
`segment 204, it may be advantageous to have a tighter
`Gaussian distribution With respect to the short side of a
`rectangular segment 204 than With respect to the long side
`of the rectangular segment 204. The 1/e2 dimension typi
`cally de?nes the Gaussian distribution, Where 1/e2 repre
`sents the percentage of poWer (91%) relative to the total
`poWer of the incoming signal. The 1/e2 dimension is chosen
`typically to lie comfortably Within the perimeter of the
`segment 204, such that excess light energy is not lost outside
`the boundaries of the segment 204. This arrangement also
`may avoid light energy spilling onto adjacent segments 204.
`The exact percentage of light energy contained Within the
`perimeter of the segment is not critical. In most
`embodiments, hoWever, most of the light energy of a light
`channel Will be con?ned Within the segment or segments
`assigned to it.
`In the embodiment that is described above, separate Ns
`are designed to be con?ned Within individual segments 204.
`In certain applications hoWever, it may be desirable to
`process multiple Ns Within a certain Wavelength band. In
`other Words, it may be advantageous to provide a certain
`type of processing upon a sub-band of 76s, Wherein the
`sub-band is subset of the entire band 206 of Wavelengths
`(Ns) being carried upon the optical signal 104.
`
`

`

`US 6,958,841 B2
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`10
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`In this application, instead of single Ns being devoted to
`each segment 204, as shoWn in FIG. 2, there could be
`multiple Ns beginning at the ?rst segment 204 Where k1 is
`shoWn, and being spaced at approximately equal intervals
`Without regard to segment boundaries. This Would alloW the
`DMD arrays Within each segment 204 to operate on multiple
`Ns simultaneously and to have approximately the same
`effect on each of them.
`For periodic pixel patterns, the resolution of the pixel
`patterns being used in the particular segments 204 are
`de?ned such that the patterns repeat a number of times
`Within the 1/e2 area of the Gaussian spot distribution. This
`alloWs the system to be less sensitive to alignment variances,
`because the overall siZe of the beam relative to any given
`periodic pattern is great. The Gaussian spot siZe might be,
`15
`for example, 20 times the siZe of a periodic pixel pattern. A
`small shift in the alignment of the Gaussian spot might then
`only shift one period relative to the 20 periods of the pixel
`pattern, but the overall aperture seen by the Gaussian spot
`Will be substantially unchanged.
`Above, both periodic and non-periodic patterns can be
`applied as starting pixel patterns that can be used for optical
`signal processing. It is possible to de?ne a number of these
`patterns that Will achieve certain characteristics and apply
`these patterns according to a look-up table based on the
`optical characteristics that are desired and the predicted
`performance characteristics of a particular pattern. In order
`to determine the predicted performance characteristics of a
`particular pattern, it Would be possible to measure the optical
`performance characteristics of those patterns.
`It is also possible to characteriZe the pixel response of
`each of the pixels Within the array, and to mathematically
`predict the optical performance of a group of pixels based on
`the phasor addition of the responses of the individual “on”
`and “off” pixels. Mathematically, the coupling of energy into
`a single-mode ?ber can be described as the summation of
`phasors as folloWs:
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`[A0413 WWW” + Ami, MOW]
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`-
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`t
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`(0.1)
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`In the above equation, the composite optical response is
`represented by Pr.
`Aon(i,j) represents the magnitude response for the pixel
`“i,j” When it is “on.” I=1 to P andj=1 to Q, if there are P roWs
`and Q columns in the array. A0 i,j) represents the magnitude
`response for the pixel “i,j” When it is “off.” By the same
`token, ¢On(i,j) and ¢O?(i,j) represent the phase responses for
`the respective “on” and “off” pixels.
`A model of the optical response characteristics of the
`various pixels in an array is illustrated in FIGS. 6A—6B. FIG.
`6A shoWs the optical response of individual “on” pixels
`taken one at a time, mapped across the entire array of pixels
`Within the segment 204. FIG. 6B shoWs the optical response
`of the individual “off” pixels taken one at a time. In addition
`to the magnitude response shoWn in FIG. 6A—FIG. 6B, there
`is also a phase effect imparted by the pixel, to the composite
`optical signal.
`Therefore, the estimated optical performance character
`istics of a group of “on” and “off” pixels are determined
`based on the sum of those pixels’ phasor responses accord
`ing to the Equation (1.1). The concept of this phasor addition
`is shoWn in FIG. 7.
`FIG. 7 is a mapping of vectors on a phasor coordinate
`system. A complex number is represented by x+jy, and that
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`complex number can be represented on a coordinate system
`by placing the x component on the horiZontal access, the Y
`component on the vertical access. The magnitude of the
`signal Will be represented by the ray that passes from the
`origin of the coordinate system to the XY point mapped onto
`that coordinate system. To add components in this coordi
`nate system, tWo vectors can be added by placing the
`beginning of one vector at the end point of another vector,
`as described above. The resulting vector Would go from the
`origin of the coordinate system to the end point of the second
`vector.
`By adding vectors in the Way described above, it is
`illustrated in FIG. 7 that the addition of tWo vectors having
`the same magnitude can cause greatly differing results
`depending on the phase angle of the particular vectors. In
`this ?gure, the sum of the “off” states are shoWn as the
`phasor from the origin to the endpoint of the last phasor AN,
`and the phasor contribution of a single “on” state pixel is
`shoWn by the vector A1(on). The resulting vector “R,” Which
`is the arroW from the origin to the end point of the A1(on)
`vector, represents the total summation of “off” and “on”
`pixels. For a given resultant background “off” state vector,
`the magnitude of the result vector “R” depends on the phase
`and magnitude of the A1(on) vector, as shoWn by the circle
`of radius |A1(on)|. The most extreme change is the differ
`ence betWeen the result vector draWn to the point on the
`circle closest to the origin of the coordinate system, to the
`point on the circle farthest from the origin of the coordinate
`system. Accordingly, to achieve the desired composition
`optical response, pixels for the patterns are chosen in this
`embodiment based both on its phase and amplitude