Signal Processing - September 2016 - 25

"Coded Aperture in X-Ray and Gamma-Ray Imaging"). In a
also cylindrical, spherical, and even flexible sensors. The
general coded aperture system, sensor measurements represent
compact form of spherical lensless cameras promise
a superposition of the images formed behind each pinhole. The
unmatched maneuverability in constrained environments
primary motivation for a coded mask is to increase the light
such as endoscopy.
throughput while retaining the ability to reconstruct high-res■ Light throughput. Lensless cameras can be designed to
olution images. For instance, if the mask contains P pinholes,
have very large input apertures, which translates into
then the sensor image is the sum of P overlapping images of the
improved light efficiency and a much larger field-of-view
scene. The signal-to-noise ratio in such an image is approxithan conventional lens-based systems.
mately P times better than a single pinhole image [2], [3].
■ Three-dimensional (3-D) imaging. Lensless imaging systems can extract 3-D and refocusing information in addition
In contrast to a single-pinhole camera, the sensor measureto two-dimensional (2-D) imaging. Although this ability is
ments of a coded aperture camera do not resemble an image of
not yet competitive with existing lens-based techniques,
the scene. Rather, each light source in the scene casts a unique
such as light-field and time of flight,
shadow of the mask onto the sensor, encodthe extracted 3-D information may still
ing information about locations and intensiLenses were introduced
be useful in some contexts, such as gesties. Consider a single light source on a dark
into cameras for
ture identification.
background; the image formed on the sensor
precisely the purpose of
In this article, we review the past, preswill be a shadow of the mask. If we change
ent, and future of lensless imaging as a shinthe angle of the light source, then the mask
increasing the size of the
ing example of the opportunities afforded
shadow on the sensor will shift. If we change
aperture, and thus the
by computational imaging, a design framethe depth of the light source, then the size of
light throughput, without
work that uses computational algorithms to
the shadow will change. We can represent
degrading the sharpness
replace or augment imaging hardware (in
the relationship between the scene and the
of the acquired image.
this case replacing the lens). After reviewsensor measurements as a linear system that
ing classical and contemporary approaches
depends on the pattern and placement of the
to lensless imaging, we introduce and analyze a mathematimask. Inverting this system using an appropriate computational
cal model that exposes the key issues underlying these
algorithm will recover an image of the scene.
architectures. The bulk of the article consists of a case study
The design of the mask plays an important role in codedof the FlatCam, a particular mask-based lensless imager we
aperture imaging. An ideal pattern would maximize the light
have developed.
throughput while providing a well-conditioned scene-tosensor transfer function to facilitate inversion. In this regard,
several mask designs have been proposed in coded aperture litEarly lensless imaging systems
erature, including Fresnel zone plate, random pinhole patterns,
uniformly redundant arrays (URAs) [3], and their extensions.
Pinhole cameras
URAs are particularly useful because of two key properties:
The very first cameras were lensless. Pinhole cameras, also
1) almost half of the mask is open, which boosts the signal-toknown as the camera obscura, were discovered centuries
noise ratio, and 2) the autocorrelation function of the mask is
before the invention of lenses and photography. Pinhole camclose to a delta function, which aids in calibration and image
eras have been well known since Alhazen (965-1039 A.D.)
recovery. URA patterns are closely related to the Hadamardand Mozi (c. 370 B.C.). However, the first photograph using a
Walsh functions and the maximum length sequences that are
pinhole camera was captured in 1850. Pinhole cameras offer a
maximally incoherent with their cyclic shifts [5].
simple and elegant architecture for lensless imaging that consists of a single aperture in front of a sensor. Light from an
object passes through the pinhole and forms its image on the
Zone plates
sensor. However, a tiny pinhole is required to produce sharp
A zone plate can also be used to focus light and form an image
images, which results in very low light throughput. As a conusing diffraction [6], [7]. A zone plate consists of concentric
sequence, a pinhole camera requires very long exposure times
transparent and opaque rings (or zones). Light hitting a zone
to acquire images at high quality. Lenses were introduced into
plate diffracts around the opaque regions and interferes concameras for precisely the purpose of increasing the size of the
structively at the focal point. Zone plates can be used in place
aperture, and thus the light throughput, without degrading the
of pinholes or lenses to form an image. One advantage of zone
sharpness of the acquired image.
plates over pinholes is their large transparent area, which provides better light efficiency. In contrast with lenses, zone plates
can be used for imaging wavelengths where lenses are either
Coded aperture cameras
expensive or difficult to manufacture [8], [9].
Coded aperture cameras extend the idea of a pinhole camera by
replacing the small, single aperture with a mask containing multiple apertures [2]-[4]. Coded aperture cameras were originally
Contemporary lensless imaging systems
invented for imaging with X-rays and gamma rays, wavelengths
Recent advances in sensor technology [in particular, the converof light that are not easily amenable to lens-based imaging (see
sion from analog film to digital charge-coupled device (CCD)
IEEE SIgnal ProcESSIng MagazInE

September 2016

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