Keywords: tdi

Summary

This demo shows how to configure a 2D array as a 1D pushbroom array with multiple stages of time-delayed integration (TDI).

Related Materials

The following demos, manuals and tutorials can provide additional information about the topics at the focus of this demo:

  • Related Demos

    • None.

  • Related Manuals

  • Related Tutorials

    • None.

Details

Time-delayed integration (TDI) is a strategy to increase signal-to-noise ratio (SNR) by effectively increasing the integration time for each pixel. Rather than using a single pixel with a long integration time, TDI uses a set of pixels that will image the same location over a period of time. This is usually utilized in a pushbroom collection system, where a 1D array is scanned across a scene using platform motion to construct the 2nd dimension of the image. TDI is typically accomplished by using a 2D array in pushbroom mode and using the 2nd dimension of that 2D array as TDI "stages" that will be used to re-image the same location as the system as the array is scanned by the platform in the along-track dimension. The figure below illustrates this concept [1].

fiete tdi diagram
Figure 1. Time-Delayed Integration Concept by Fiete.

Important Files

The focus of this demo is to compare different sensor configurations and the impacts of noise in those configurations. The noise is introduced by the built-in detector model available in the DIRSIG5 BasicPlatform plugin. Below is the baseline temporal integration and detector model configuration in the .platform file that is manipulated across the various simulations.

          <focalplane>
            <capturemethod>
              <imagefile areaunits="cm2" fluxunits="photonspersecond">
                <basename>short_int</basename>
                <extension>img</extension>
                <schedule>simulation</schedule>
                <datatype>12</datatype>
              </imagefile>
              ...
              <temporalintegration tdi="false">
                <time>2.0e-05</time>
                <samples>1</samples>
              </temporalintegration>
              <detectormodel>
                <quantumefficiency>1.0</quantumefficiency>
                <readnoise>20</readnoise>
                <darkcurrentdensity>8.0e-07</darkcurrentdensity>
                <minelectrons>0</minelectrons>
                <maxelectrons>10e+02</maxelectrons>
                <bitdepth>12</bitdepth>
              </detectormodel>
              ...
            </capturemethod>
            <detectorarray spatialunits="microns">
              <clock type="independent" temporalunits="hertz">
                <rate>50000</rate>
                <offset>0</offset>
              </clock>
              <xelementcount>250</xelementcount>
              <yelementcount>1</yelementcount>
              <xelementsize>2.00000</xelementsize>
              <yelementsize>2.00000</yelementsize>
              <xelementspacing>2.00000</xelementspacing>
              <yelementspacing>2.00000</yelementspacing>
              <xarrayoffset>0.000000</xarrayoffset>
              <yarrayoffset>0.000000</yarrayoffset>
              <xflipaxis>1</xflipaxis>
              <yflipaxis>0</yflipaxis>
            </detectorarray>
          </focalplane>

The array clock rate for all the sensors is 50 kHz (see the <clock> element), which means the array is read out every 20 microseconds (1 / 50000 = 20e-06 seconds).

Since the A/D convertor is setup to produce 12-bit data (see the <bitdepth> element), the output image <datatype> has been set to 12, which corresponds to 16-bit unsigned integer data.

Note that the tdi attribute in the <temporalintegration> is what controls if the Y dimension of the array is used for TDI.

The noise sources (Shot noise, dark current noise and read noise) are constant across all the simulations. The key parameters that will be manipulated are related to the array dimensions, temporal integration and the enabling of TDI. The table below summarizes the differences between the four simulations included in this demo:

Table 1. Sensor Configurations
Name Array Size Integration Time Max Electrons TDI Flag

no_noise.platform

250 x 1

N/A

N/A

N/A

short_int.platform

250 x 1

2.0e-05

1000

false

long_int.platform

250 x 1

1.6e-04

8000

false

tdi.platform

250 x 8

2.0e-05

8000

true

No Noise

The baseline in this demo is the "no noise" simulation, which uses a 1D array without temporal integration (radiance mode) and without the detector model configured. The resulting image features no blurring due to any temporal integration (motion related) effects and has no noise.

Short Integration Time

The detector array in this scenario only has a single row of pixels. The short integration time setup uses a 20 microsecond integration time and the A/D convertor has the max electrons set to 1000. This simulation will exhibit a baseline signal-to-noise ratio (SNR).

Long Integration Time

The detector array in this scenario also has a single row of pixels. The long integration time setup uses a 160 microsecond integration time, which is 8x longer than the short integration time. Since it will integrate 8x more signal, the A/D convertor max electrons is set to 8000, which is 8x larger than the short integration scenario. The goal of the longer integration time is to reduce the baseline SNR. However, the longer integration time will impact the image quality by blurring the image in the along track direction.

Time Delayed Integration

The detector array in this scenario has 8 rows of pixels that will be used for the time-delayed integration. The integration time for this setup is the same as the short integration setup, but to achieve a similar SNR as the 8x longer integration time the sensor uses those 8 rows of pixels as 8 stages of TDI. Since the effective integration time (across all 8 stages) is 8x longer than the short integration time, the A/D max electons is the same as the long integration time value of 8000.

Note
 The number of TDI stages is a user-defined parameter supplied directly via the Y dimension (the default along-track) of the detector array. The 8 stages used in this example is arbitrary. Modern commercial systems (e.g. WorldView-3) can feature as many as 32 stages of TDI in some band arrays.

Setup

To run the four simulations, perform the following steps:

  1. Run the DIRSIG no_noise.jsim file.

  2. Run the DIRSIG short_int.jsim file.

  3. Run the DIRSIG long_int.jsim file.

  4. Run the DIRSIG tdi.jsim file.

Note
 Because these are advanced DIRSIG5 simulations using JSIM configurations, the simulations need to be run from the command line.

Results

The output images from the simulations are shown below (scaled using a simple min/max scaling):

The output of the no_noise, short_int, long_int and tdi simulations (left to right).

no noise short int long int tdi

The no_noise image reflects the pristine (ideal) image that we would expect. There are no temporal integration blurring effects (from either sensor or scene motion), however the spinning rotor on the helicopter are slightly distorted due to the time offset from line-to-line in this pushbroom-style collection. In addition, there is no noise present in the simulation. This is best observed in the uniform, white areas of the target panels which feature no variation. Note that in the "radiance mode" used by this simulation, even photon arrival (aka Shot noise) is not included in the simulation.

The short_int output includes the impacts of both temporal integration and the detector model noise sources. The most obvious impact is due to the detector model noise, which is introducing significant variation across the scene. This is most easily observed in the white areas of the target panels.

The long_int output shows the expected improvement in the noise (again, most easily observed in the white areas of the target panels). However, the long integration time is so long that there is a significant amount of blurring in the along-track (vertical) axis of the image.

The tdi output illustrates the advantage of this approach, by featuring the reduced noise levels of the long integration time but with the lack of blurring effects seen in the short integration time scenario. However that TDI will still introduce blurring effects in moving objects like the helicopter rotor blades.

The table below contains the mean and standard deviation for a region of the white part of the tr-bar target from each simulation.

Table 2. Statistics for the white panel.
Name Mean (counts) Stddev (counts)

Short (1x) Integration

1.292422e+03

1.094757e+02

Long (8x) Integration

1.281355e+03

7.143720e+01

TDI 8 stages

1.295832e+03

2.770331e+01

The mean values for all the simulations are the same. Note that without the change in the A/D max electrons for the long integration and TDI simulations, those two simulations would have a mean that is 8x greater than the short integration since they have effectively an 8x longer integation time. The standard deviation for the short integration is the highest. The long integration reduces the noise by 1.5x and the TDI approaches reduces is by 3.9x. If the noise is normally distributed we would expect the noise to reduce by the square root of the increased integration time (sqrt(8) = 2.828).

1. Robert Fiete, "Modeling the imaging chain of digital cameras"', Tutorial Texts in Optical Engineering, TT92, SPIE Press, 2010