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 1. Analog Dialogue Technical Journal
 2. Articles
 3. ToF System Design—Part 2: Optical Design for Time of Flight Depth Sensing
    Cameras


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 * AUG 2021
   VOL 55
 * 




TOF SYSTEM DESIGN—PART 2: OPTICAL DESIGN FOR TIME OF FLIGHT DEPTH SENSING
CAMERAS

by Tzu-Yu Wu Download PDF


ABSTRACT

Optics plays a key role in time of flight (ToF) depth sensing cameras, and the
optical design dictates the complexity and feasibility of the final system and
its performance. 3D ToF cameras have certain distinct characteristics1 that
drive special optics requirements. This article presents the depth sensing
optical system architecture—which consists of the imaging optics sub-assembly,
the ToF sensor on the receiver, and the illumination module on the
transmitter—and discusses how to optimize each sub-module to improve the sensor
and system performance.


INTRODUCTION

ToF is an emerging 3D sensing and imaging technology that has found numerous
applications in areas such as autonomous vehicles, virtual and augmented
reality, feature identification, and object dimensioning. ToF cameras acquire
depth images by measuring the time it takes the light to travel from a light
source to objects in the scene and back to the pixel array. The specific type of
technology that Analog Devices’ ADSD3100 backside illuminated (BSI) CMOS sensor
implements is called continuous wave (CW) modulation, which is an indirect ToF
sensing method. In a CW ToF camera, the light from an amplitude modulated light
source is backscattered by objects in the camera’s field of view (FOV), and the
phase shift between the emitted waveform and the reflected waveform is measured.
By measuring the phase shift at multiple modulation frequencies, one can
calculate a depth value for each pixel. The phase shift is obtained by measuring
the correlation between the emitted waveform and the received waveform at
different relative delays using in-pixel photon mixing demodulation.2 The
concept of CW ToF is shown in Figure 1.

Figure 1. The concept of ToF technology.


DEPTH SENSING OPTICAL SYSTEM ARCHITECTURE

Figure 2 shows the optical system architecture. It can be broken down into two
main sub-module categories: imaging module (also known as receiver or Rx) and
illumination module (also known as transmitter or Tx). The following sections
introduce the function of each component, requirements distinct to the ToF
system, and corresponding design examples.


ILLUMINATION MODULE

The illumination module consists of a light source, a driver that drives the
light source at a high modulation frequency, and a diffuser that projects the
optical beam from the light source to the designed field of illumination (FOI),
as illustrated in Figure 2.

Figure 2. An example of a ToF optical system architecture cross-section.

LIGHT SOURCE AND DRIVER

ToF modules normally use light sources that are narrow band with low temperature
dependence of the wavelength, including vertical cavity surface emitting lasers
(VCSELs) and edge emitting lasers (EELs). Light emitting diodes (LEDs) are
generally too slow for ToF modulation requirements. VCSELs have gained more
popularity over recent years due to their lower cost, form factor, and
reliability, along with being easy to integrate into ToF modules. Compared with
EELs (that emit from the side) and LEDs (that emit from the sides and top),
VCSELs emit beams perpendicular to their surface, which offers better yield in
production and lower fabrication cost. In addition, the desired FOI can be
achieved by using a single engineered diffuser with the designed divergence and
optical profile. The optimization of the laser driver, as well as the electrical
design and layout of the printed circuit boards (PCBs) and light source are
critically important to achieve high modulation contrast and high optical power.

ILLUMINATION WAVELENGTH (850 NM VS. 940 NM)

While the ToF operational principle does not depend on the wavelength (rather it
depends on the speed of light) and therefore the wavelength should not affect
the accuracy, the choice of wavelength can affect the system-level performance
in some use cases. The following are some considerations when choosing the
wavelength.

 * Sensor quantum efficiency and responsivity:

Quantum efficiency (QE) and responsivity (R) are linked to each other.

 * QE measures the ability of a photodetector to convert photons into electrons.

 * R measures the ability of a photodetector to convert optical power into
   electric current

where q is electron charge, h is plank constant, c is speed of light, and λ is
wavelength.

Typically, the QE of silicon-based sensors is about 2× better or more at 850 nm
than at 940 nm. For example, ADI CW ToF sensors have 44% QE at 850 nm and 27% QE
at 940 nm. For the same amount of illumination optical power, higher QE and R
lead to better signal-to-noise ratio (SNR), especially when not much light
returns to the sensor (which is the case for faraway or low reflectivity
objects).

 * Human perception

While the human eye is insensitive in the near infrared (NIR) wavelength range,
light at 850 nm can be perceived by the human eye. On the other hand, 940 nm is
invisible to the human eye.

 * Sunlight

Although the solar emission is maximum in the visible region of the spectrum,
the energy in the NIR region is still significant. Sunlight (and ambient light
more generally) can increase depth noise and reduce the range of a ToF camera.
Fortunately, due to atmospheric absorption, there is a dip in sunlight
irradiance in the 920 nm to 960 nm region, where the solar irradiance is less
than half compared to the 850 nm region (see Figure 3). In outdoor applications,
operating the ToF system at 940 nm provides better ambient light immunity and
leads to better depth sensing performance.

Figure 3. Solar spectral irradiance in NIR.3

RADIANT INTENSITY (OPTICAL POWER PER SOLID ANGLE)

The light source generates a constant optical power distributed into a 3D space
within the FOI produced by the diffusing optics. As the FOI increases, the
energy sustained per steradian (sr)—that is, radiant intensity [W/sr]—decreases.
It is important to understand the trade-offs between FOI and radiant intensity
as they affect the SNR, and therefore the depth range, of the ToF system.

Table 1 lists a few examples of FOI and their corresponding radiant intensity
normalized to the radiant intensity of a 60° × 45° FOI. Note that the radiant
intensity is calculated as optical power per rectangular solid angle.

Table 1. Normalized Radiant Intensity Case Horizontal FOI Vertical FOI
Normalized Radiant Intensity 1 60° 45° 100% 2 52° 52° 100% 3 60° 60° 76% 4 72°
58° 67% 5 78° 65° 56%

ILLUMINATION PROFILE SPECIFICATIONS

To fully define the illumination profile, several characteristics should be
clearly specified including the profile shape, profile width, optical efficiency
(that is, enclosed energy within a certain FOV), and optical power drop-off
outside the FOI. The illumination profile specification is normally defined in
radiant intensity in angular space. Mathematically it is expressed as:

where dΦ is the power emitted into the solid angle dΩ. The FOI needs to match
the aspect ratio of the imager, and hence is normally square or rectangular.

 * Illumination profile shape inside FOI

The most common radiant intensity profiles in ToF flood illumination have a
batwing shape. They have a profile that varies in cos-n (θ) to compensate for
the drop-off (that is, relative illumination) of the imaging lens. Figure 5
demonstrates an example of a batwing illumination profile. If one wishes to
achieve constant irradiance on the pixel array of the imager from a flat target,
one should also consider a cos3 (θ) drop-off factor in irradiance (E) between
the target center and the target edge [W/m2], which is defined as:

where E is irradiance, dA is the surface area illuminated by optical power dΦ,
R(θ) is the distance between the light source to dA defined in Figure 4, and dΩ
= dAcos(θ)/R(θ)2.

Figure 4. Irradiance distribution vs. intensity.
 * Width of the profile

The width of the profile determines the FOI of the illumination profile. It can
be defined as full width half max or 1/e2 of the maximum intensity. To
accommodate misalignment between the imaging lens to the imager and the
tolerance of the diffuser, FOI is normally designed to be slightly larger than
the FOV of the lens to avoid dark pixels.

The width of the profile is the convolution of the intensity profile of the
light source to the diffuser response to a collimated beam. The wider the input
divergence angle to the diffuser, the wider the width and slower the transition
slope. A wider and slower transition slope results in more energy falling
outside the FOI, which causes optical power loss. The acceptance criteria for
such loss can be specified using the following two requirements.

 * Optical efficiency—enclosed energy within the imaging lens FOV

This specification defines how much energy will be received by the imaging
module and is specified by:

Figure 5c illustrates the concept of 2D integration of the illumination profile
within FOV.

 * Optical power drop-off outside FOI

Figure 5. An illumination profile example.

In general, the optical efficiency can be improved by having a collimator lens
between the light source and the diffuser to reduce the input angle to the
diffuser, or by choosing a light source with a smaller divergence angle.


IMAGING MODULE

The imaging module consists of an imaging lens assembly, band-pass filter (BPF),
and microlens array on the imager. The thickness and material of the backside
optical stacks on the imager should be optimized for low back-reflection. Figure
6 shows an illustration of the imaging module.

Figure 6. Illustration of the imaging module.

TOF IMAGING LENS DESIGN CONSIDERATIONS

Since the ToF camera collects light generated by active illumination, the
efficiency and uniformity of the light collection on the pixel array greatly
affect the overall performance. The lens needs to have a strong collecting
power, high transmission, and low stray light. The following are design
considerations for ToF lenses, which are distinct from traditional RGB camera
lenses.

 * Light collecting efficiency

Light collection efficiency is proportional to 1/(f/#)2, where f/# = (focal
length)/(aperture size). The smaller the f/#, the better the efficiency. There
are some trade-offs with a small f/# optical system. As the aperture size
increases, there tend to be more vignetting and aberrations, which make the
optics more challenging to design. A low f/# system also tends to have shallower
depth of field.

 * Relative illumination (RI) and chief ray angle (CRA)

RI is defined as:

The sensor illuminance declines based on the (cos q)4 law, in a distortion and
vignetting free lens system where q is the CRA incident angle on the sensor
plane. The result is a relative darkening of the image toward the sensor border.
The irradiance fall-off can be reduced by introducing negative distortion in the
lens system.

The max CRA at the sensor edge should be optimized based on the imager microlens
array specification. A smaller CRA helps narrow the bandwidth of the BPF to
achieve better ambient light immunity.

The following examples demonstrate how the CRA and the focused light cone sizes
(effective f/#) across the field affect the RI. The lens system of Example 1 in
Figure 7 has larger CRAs and gradually decreasing imaging cones (that is,
increased f/#) as the field angle increases. The corresponding RI drops
significantly with the field angle as shown in the corresponding RI plot.
Example 2 in Figure 7 demonstrates that the RI can be well maintained by
minimizing the CRA as well as keeping uniform f/# across the field.

 * Stray light

Stray light is any unintended light in a system that could be detected by the
sensor. Stray light can come from in or out of field sources that form a ghost
image (for example, lens flare) through even numbers of reflections. Stray light
can also emanate from opto-mechanical structures and any scattering surfaces.
ToF systems are particularly sensitive to stray light because the multipath
nature of stray light contributes different optical path lengths to a pixel,
which leads to depth measurement inaccuracies. Several strategies in the design
process need to be used to reduce stray light, such as optimization of the
anti-reflection (AR) coating and the mechanical aperture, darkening the lens
edges and mounting structures, and custom design of the BPF to optimize for
wavelength and CRA.

The following are some items that can impact stray light in a system:

 * Vignetting

Ideally there should not be any vignetting in a ToF lens system. Vignetting cuts
off the imaging rays and is sometimes used as a technique to increase the image
quality while trading off the brightness of the peripheral fields. However, the
cutoff rays often bounce inside the lens system and tend to cause stray light
issues.

 * AR coating

AR coating on the optical elements reduces the reflectance of each surface and
can effectively reduce the impact of lens reflections on depth calculation. AR
coatings should be carefully designed for the light source wavelength range and
the angle range for the incident angles on the lens surfaces.

 * Number of lens elements

Although adding more lens elements provides more freedom to achieve the design
specifications and better image quality in terms of resolution, it also
increases the inevitable back reflections from the lens elements as well as
increasing complexity and cost.

 * Band-pass filter (BPF)

The BPF cuts off ambient light contribution and is essential for ToF systems.
The BPF design should be tailored to the following parameters to have the best
performance.

(a) Lens parameters such as f/# and CRA across the field

(b) Light source parameters such as bandwidth, nominal wavelength tolerance, and
thermal shift

(c) Substrate material properties to low incident angle drift vs. wavelength or
low thermal drift vs. wavelength

 * Microlens array

A ToF backside illuminated (BSI) sensor normally has a layer of microlens array
that converges rays incident to the image sensor and maximizes the number of
photons that reach the pixel modulation region. The geometry of the microlens is
optimized to achieve the highest absorption within the pixel region where
photons are converted into electrons.

Figure 7. Relative illumination examples.

In many lens designs, the CRA of the lens increases as the image height
increases toward the edge of the sensor, as shown in Figure 8. This oblique
incidence leads to absorption loss in the pixel and crosstalk between adjacent
pixels when the CRA is too big. It is important to design or choose an imaging
lens such that the CRA of the lens matches the specifications of the microlens
array it is designed for. For example, the optimal CRA that matches with ADI ToF
sensor ADSD3100 is at around 12° at the sensor horizontal and vertical edges.

Figure 8. Max CRA of an imaging lens.


CONCLUSION

ToF optics have unique requirements to achieve optimal performance. This article
provides an overview of a 3D ToF camera optical architecture and design
guidelines for the illumination and imaging sub-modules to help design such
optical systems and/or choose sub-components. For the illumination sub-module,
the key factors are power efficiency, reliability, and the ability of the light
source to be driven at high modulation frequency with high modulation contrast.
Wavelength selection consideration between 850 nm and 940 nm, as well as how to
specify the illumination profiles are discussed in detail. For the imaging
sub-module, the lens design considerations including f/#, CRA that matches with
the microlens specification, and stray light control are critical to
system-level performance.


REFERENCES

1 Paul O’Sullivan and Nicolas Le Dortz. “Time of Flight System Design—Part 1:
System Overview.” Analog Dialogue, Vol. 55, No. 3, July 2021.

2 Cyrus S. Bamji, Swati Mehta, Barry Thompson, Tamer Elkhatib, Stefan Wurster,
Onur Akkaya, Andrew Payne, John Godbaz, Mike Fenton, Vijay Rajasekaran, Larry
Prather, Satya Nagaraja, Vishali Mogallapu, Dane Snow, Rich McCauley, Mustansir
Mukadam, Iskender Agi, Shaun McCarthy, Zhanping Xu, Travis Perry, William Qian,
Vei-Han Chan, Prabhu Adepu, Gazi Ali, Muneeb Ahmed, Aditya Mukherjee, Sheethal
Nayak, Dave Gampell, Sunil Acharya, Lou Kordus, and Pat O’Connor. “IMpixel 65nm
BSI 320MHz demodulated TOF Image sensor with 3μm global shutter pixels and
analog binning.” 2018 IEEE International Solid-State Circuits Conference
(ISSCC), February 2018.

3 “Reference Air Mass 1.5 Spectra.” National Renewable Energy Laboratory.


AUTHOR

Tzu-Yu Wu



Tzu-Yu Wu is a senior optical design engineer at Analog Devices. She leads ADI’s
optics development for time of flight (ToF) technology and has been working on
optical designs for imaging lens, illumination optics, stray light analysis, and
optimizations on the microlens array and the optical stacks of the backside
illuminated CMOS ToF sensor. Prior to joining ADI, she had worked at Canon
U.S.A. to develop advanced medical imaging systems such as ultra-miniature
endoscopes and cardiovascular imaging catheters. She earned her Ph.D. and M.S.
degrees in optical sciences from the University of Arizona, and an M.S. degree
in physics from National Taiwan University. Her Ph.D. research focused on the
development of high resolution imaging devices that provide rapid detection of
early stage cancer through minimally invasive procedures.


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