Signal Processing - September 2016 - 30

xk-3

xk-2

xk-1
xk+1
xk

Separable Mask
on Sensor

Screen

Separable Hadamard
Patterns

(a)
T

Sensor Measurements: Y = ΦL × ΦR

Horizontal
Patterns
Yield

Vertical
Patterns
Yield

Left System
Matrix

Right
System
Matrix
T

ΦL

ΦR
(b)

Figure 4. Calibration for measuring the left and right matrices U L and U R corresponding to a separable mask. (a) Separable patterns displayed on a
screen in front of the camera. The patterns are orthogonal, one-dimensional Hadamard codes that are repeated along either the horizontal or vertical
direction. (b) Estimated left and right matrices. (Figure modified from [31] and used with permission.)

Prototypes
We have built two different FlatCam prototypes. The first
prototype consists of a Point Grey Flea3 with a Sapphire
EV76C560 CMOS sensor, which has a 5.3-μm pixel size and
measured Chief Ray Angle (CRA) of 25°. (The CRA of a sensor determines the cone of light that can enter a pixel.) The
diffractive mask is chrome on quartz glass placed adjacent
to the infrared filter of the sensor (mask-to-sensor distance:
1.2 mm). The pattern on the mask is an outer product of two
length-1024 pseudorandom sequences of smallest feature
size 25 μm. Sample reconstructions using this prototype are
shown in Figure 5(a). Reconstructions of a dynamic scene
are shown in Figure 5(b); here, we operated the camera with
a 3 ms exposure and recovered videos of 60 frames per second with each frame of the video recovered independently as
a stand-alone image.
The second prototype was assembled with a diffractive mask
and spacer attached directly to the surface of an Omnivision
OV5647 CMOS sensor (fourth example of lensless in Figure 1).
The Omnivision sensor has pixels of size 1.4 μm and measured
CRA of 28°. The diffractive mask was fabricated by depositing
a thin-film of chrome on fused silica that was then patterned
with photoresist and etched to leave the desired pattern. The
mask was then diced, aligned to the CMOS pixel array, and
30

attached with optical epoxy (mask to sensor distance 500 μm).
The pattern on the mask is the outer product of length-1296
and 972 pseudorandom sequences of smallest feature size of
2.8 μm. The smaller feature size and pixel pitch of this prototype enable reconstructions at a higher resolution. However,
a drawback of the smaller pixel pitch is a sensor with poorer
SNR performance, which results in noisier measurements and
reconstruction compared to our first prototype (see Figure 6).
The remainder of the examples below were obtained using
the higher-quality Flea3 sensor prototype.

Programmable masks
In many applications, a camera has the opportunity to acquire
several images of a scene, and both folk wisdom and theory
tell us that averaging the acquisitions should suppress noise.
In contrast to a lens-based camera, a lensless camera could be
equipped with a programmable mask that changes for each
acquisition to provide diversity in the acquisitions. Presumably,
such a camera should not only suppress noise but also average
out imperfections in the measurement operator U (recall that U
is never perfectly conditioned in a coded aperture system).
To demonstrate the potential of a programmable mask
FlatCam, we simulated multi-image capture using the sequences of separable measurement matrices {U L i} i = 1,.., L and

IEEE SIgnal ProcESSIng MagazInE

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September 2016

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Table of Contents for the Digital Edition of Signal Processing - September 2016

Signal Processing - September 2016 - Cover1
Signal Processing - September 2016 - Cover2
Signal Processing - September 2016 - 1
Signal Processing - September 2016 - 2
Signal Processing - September 2016 - 3
Signal Processing - September 2016 - 4
Signal Processing - September 2016 - 5
Signal Processing - September 2016 - 6
Signal Processing - September 2016 - 7
Signal Processing - September 2016 - 8
Signal Processing - September 2016 - 9
Signal Processing - September 2016 - 10
Signal Processing - September 2016 - 11
Signal Processing - September 2016 - 12
Signal Processing - September 2016 - 13
Signal Processing - September 2016 - 14
Signal Processing - September 2016 - 15
Signal Processing - September 2016 - 16
Signal Processing - September 2016 - 17
Signal Processing - September 2016 - 18
Signal Processing - September 2016 - 19
Signal Processing - September 2016 - 20
Signal Processing - September 2016 - 21
Signal Processing - September 2016 - 22
Signal Processing - September 2016 - 23
Signal Processing - September 2016 - 24
Signal Processing - September 2016 - 25
Signal Processing - September 2016 - 26
Signal Processing - September 2016 - 27
Signal Processing - September 2016 - 28
Signal Processing - September 2016 - 29
Signal Processing - September 2016 - 30
Signal Processing - September 2016 - 31
Signal Processing - September 2016 - 32
Signal Processing - September 2016 - 33
Signal Processing - September 2016 - 34
Signal Processing - September 2016 - 35
Signal Processing - September 2016 - 36
Signal Processing - September 2016 - 37
Signal Processing - September 2016 - 38
Signal Processing - September 2016 - 39
Signal Processing - September 2016 - 40
Signal Processing - September 2016 - 41
Signal Processing - September 2016 - 42
Signal Processing - September 2016 - 43
Signal Processing - September 2016 - 44
Signal Processing - September 2016 - 45
Signal Processing - September 2016 - 46
Signal Processing - September 2016 - 47
Signal Processing - September 2016 - 48
Signal Processing - September 2016 - 49
Signal Processing - September 2016 - 50
Signal Processing - September 2016 - 51
Signal Processing - September 2016 - 52
Signal Processing - September 2016 - 53
Signal Processing - September 2016 - 54
Signal Processing - September 2016 - 55
Signal Processing - September 2016 - 56
Signal Processing - September 2016 - 57
Signal Processing - September 2016 - 58
Signal Processing - September 2016 - 59
Signal Processing - September 2016 - 60
Signal Processing - September 2016 - 61
Signal Processing - September 2016 - 62
Signal Processing - September 2016 - 63
Signal Processing - September 2016 - 64
Signal Processing - September 2016 - 65
Signal Processing - September 2016 - 66
Signal Processing - September 2016 - 67
Signal Processing - September 2016 - 68
Signal Processing - September 2016 - 69
Signal Processing - September 2016 - 70
Signal Processing - September 2016 - 71
Signal Processing - September 2016 - 72
Signal Processing - September 2016 - 73
Signal Processing - September 2016 - 74
Signal Processing - September 2016 - 75
Signal Processing - September 2016 - 76
Signal Processing - September 2016 - 77
Signal Processing - September 2016 - 78
Signal Processing - September 2016 - 79
Signal Processing - September 2016 - 80
Signal Processing - September 2016 - 81
Signal Processing - September 2016 - 82
Signal Processing - September 2016 - 83
Signal Processing - September 2016 - 84
Signal Processing - September 2016 - 85
Signal Processing - September 2016 - 86
Signal Processing - September 2016 - 87
Signal Processing - September 2016 - 88
Signal Processing - September 2016 - 89
Signal Processing - September 2016 - 90
Signal Processing - September 2016 - 91
Signal Processing - September 2016 - 92
Signal Processing - September 2016 - 93
Signal Processing - September 2016 - 94
Signal Processing - September 2016 - 95
Signal Processing - September 2016 - 96
Signal Processing - September 2016 - 97
Signal Processing - September 2016 - 98
Signal Processing - September 2016 - 99
Signal Processing - September 2016 - 100
Signal Processing - September 2016 - 101
Signal Processing - September 2016 - 102
Signal Processing - September 2016 - 103
Signal Processing - September 2016 - 104
Signal Processing - September 2016 - 105
Signal Processing - September 2016 - 106
Signal Processing - September 2016 - 107
Signal Processing - September 2016 - 108
Signal Processing - September 2016 - 109
Signal Processing - September 2016 - 110
Signal Processing - September 2016 - 111
Signal Processing - September 2016 - 112
Signal Processing - September 2016 - 113
Signal Processing - September 2016 - 114
Signal Processing - September 2016 - 115
Signal Processing - September 2016 - 116
Signal Processing - September 2016 - 117
Signal Processing - September 2016 - 118
Signal Processing - September 2016 - 119
Signal Processing - September 2016 - 120
Signal Processing - September 2016 - 121
Signal Processing - September 2016 - 122
Signal Processing - September 2016 - 123
Signal Processing - September 2016 - 124
Signal Processing - September 2016 - 125
Signal Processing - September 2016 - 126
Signal Processing - September 2016 - 127
Signal Processing - September 2016 - 128
Signal Processing - September 2016 - 129
Signal Processing - September 2016 - 130
Signal Processing - September 2016 - 131
Signal Processing - September 2016 - 132
Signal Processing - September 2016 - 133
Signal Processing - September 2016 - 134
Signal Processing - September 2016 - 135
Signal Processing - September 2016 - 136
Signal Processing - September 2016 - 137
Signal Processing - September 2016 - 138
Signal Processing - September 2016 - 139
Signal Processing - September 2016 - 140
Signal Processing - September 2016 - 141
Signal Processing - September 2016 - 142
Signal Processing - September 2016 - 143
Signal Processing - September 2016 - 144
Signal Processing - September 2016 - 145
Signal Processing - September 2016 - 146
Signal Processing - September 2016 - 147
Signal Processing - September 2016 - 148
Signal Processing - September 2016 - 149
Signal Processing - September 2016 - 150
Signal Processing - September 2016 - 151
Signal Processing - September 2016 - 152
Signal Processing - September 2016 - 153
Signal Processing - September 2016 - 154
Signal Processing - September 2016 - 155
Signal Processing - September 2016 - 156
Signal Processing - September 2016 - 157
Signal Processing - September 2016 - 158
Signal Processing - September 2016 - 159
Signal Processing - September 2016 - 160
Signal Processing - September 2016 - 161
Signal Processing - September 2016 - 162
Signal Processing - September 2016 - 163
Signal Processing - September 2016 - 164
Signal Processing - September 2016 - 165
Signal Processing - September 2016 - 166
Signal Processing - September 2016 - 167
Signal Processing - September 2016 - 168
Signal Processing - September 2016 - 169
Signal Processing - September 2016 - 170
Signal Processing - September 2016 - 171
Signal Processing - September 2016 - 172
Signal Processing - September 2016 - 173
Signal Processing - September 2016 - 174
Signal Processing - September 2016 - 175
Signal Processing - September 2016 - 176
Signal Processing - September 2016 - Cover3
Signal Processing - September 2016 - Cover4
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