Signal Processing - September 2016 - 27

The lensless camera in [11] (the first example of lensless in
Figure 1) uses compressive sensing principles to capture and
recover images. It consists of a single programmable SLM and
a single pixel detector. It captures multiple measurements of the
scene by changing the mask pattern. The scene is then reconstructed by solving a sparse recovery program. Using multiple
pixel detectors, this design can reconstruct a higher resolution
image for a planar or a sufficiently distant scene [13].
The camera in [12] consists of a sensor array and an SLM
implementing a separable mask pattern. This camera can
reconstruct the scene using a single sensor image, but the
reconstruction quality improves using multiple sensor images
with different mask patterns. In the development of this camera, the authors showed that traditional techniques [3] of using
URA and modified URA (MURA) aperture patterns fail due
to significant diffraction effects in the visible spectrum.

Amplitude
Mask

Lensless microscopy via shadow and diffraction imaging
Lensless cameras have also been successfully demonstrated
for several microscopy and lab-on-chip applications. We can
divide the lensless microscopes into two broad categories: contact-mode shadow imaging-based microscopes [19]-[21] and
diffraction-based lensless microscopes [22]-[27]. In a shadow
imaging-based microscope, a microscopic sample is placed
extremely close to a sensor array (ideally within 1 nm) so that
diffraction is minimized. Light from an illumination source
passes through the sample and casts a shadow on the sensor
with unit magnification. The shadow image represents the
image of the microscopic sample under observation. It is also
possible to capture multiple images of a sample with subpixel
shifts for the purpose of digital superresolution. The on-chip

∆

ω
ω

Image
Sensor

∆

Legend
x-Axis

d - Mask to Sensor Distance
∆ - Mask Feature Size
ω - Pixel Pitch
z-Axis

Ultra-miniature lensless imaging with diffraction gratings
Ultra-miniature cameras (approximately 100 n m width and
thickness) have been implemented in [14]-[17] using integrated diffraction gratings and CMOS image sensors. The pixels
in [14] use diffraction gratings over a photodiode in order to
be sensitive to the angle of incident light. The angle selectivity
is achieved due to a phenomenon called the Talbot effect [18]
and enables the camera to perform lensless 3-D imaging in the
near field. The gratings were fabricated as metal wiring layers
over the photodiodes.
The phase gratings in [16] are designed such that they
impose spiral-shaped diffraction patterns (the second example
for lensless in Figure 1) on the sensor array. The diffraction
pattern is etched on a refractive medium placed above the sensor. The spiral pattern can also be viewed as the point spread
function of these imaging systems. Similar to a coded aperture
system, the image formed on the sensor is a superposition of
shifted and scaled spiral patterns. However, in contrast to an
amplitude mask, a phase grating-based mask has improved
light efficiency, since it blocks much less light. While an image
of the scene can be recovered using a computational algorithm,
the primary purpose of these small-size and low-cost designs
is distributed monitoring and inspection (for example, in the
Internet of Things).

∆

Figure 2. A schematic of a lensless imager using a single amplitude mask.

microscope in [20] demonstrated imaging of red blood cells at
a resolution of 600 nm by combining multiple low-resolution
shadow images of blood flowing in a microfluidic channel.
Diffraction-based lensless microscopes allow a significant distance between the sample and the sensor plane. Light
scattered by the sample interferes with itself and creates an
interference pattern on the sensor (the third example of lensless in Figure 1). These interference patterns can be digitally
processed to reconstruct an image of the sample [24], [25]. The
on-chip microscope in [25] demonstrated imaging of red blood
cells at a resolution less than 7 nm with a field-of-view of
20.5 mm2. Since the optical sensor records only the intensity
of the interference patterns and loses the phase information,
image reconstruction relies on computational methods for
phase retrieval [28], [29].

A mathematical model for lensless imaging
A simple mathematical model can be used to explain, characterize, and analyze the operation of a variety of lensless imagers.

Lensless imaging architecture
Consider the imaging architecture in Figure 2, which consists
of an amplitude mask placed in front of an image sensor. Both
the sensor and the mask are assumed to be planar and parallel
to each other. The mask is placed a distance d (typically measured in microns) in front of the sensor; hence, we can assume
the sensor is placed on the plane z = 0 and the mask on the
plane z = d. Assume, without loss of generality, that the mask
is binary-valued and consists of opaque and transparent elements that either block or transmit light. An important variable is the smallest feature size on the mask, Δ; intuitively, the
binary mask is constructed using opaque or transparent building blocks of size D # D. Denote the pixel pitch, or the size
of individual sensor pixels, by w. Given this basic setup, we
can characterize the spot size produced by a mask element and

IEEE SIgnal ProcESSIng MagazInE

September 2016

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