**3. SiGe sensor performance modeling**

#### **3.1. Performance model overview**

This section deals with modeling of SiGe NIR FPA imaging performance over a wide range of light levels that can occur for day-night operation [13]. The model predicts detector dark currents, photocurrents, and readout and background noise associated with a novel small pixel, low-cost SiGe visible-NIR prototype camera. This type of imager, based on the ability to grow NIR-sensitive SiGe layers on silicon to form pixels utilizing existing high quality and low-cost semiconductor and electronic architectures, is intended to provide NIR night vision capability in addition to visible operation.

A fairly large matrix of variables, which include NIR background, pixel size, focal length, *f*number, integration time, spectral bandpass, dark current level, and readout noise level, require a significantly complex model to perform the necessary design trade studies. This model predicts values for sensor noise equivalent intensity (NEI) and SNR, and also generates simulated 30 and 60 Hz NIR image sequences. The model was designed to assist in the development of miniature NIR or visible-NIR cameras and FPA designs and predict NEI and SNR performance of image or video quality (resolution and noise), so as to aid in the design of SiGe detector based camera optics, FPA formats, readout electronics, and pixel size.

#### **3.2. Variable NIR background**

dark currents and the readout noise must be added.

mechanical, and optical analyses of encapsulation and optical materials to enable compatibility

**Figure 3.** SiGe technology is associated with a number of military applications involving NIR sensitivity, including

This section deals with modeling of SiGe NIR FPA imaging performance over a wide range of light levels that can occur for day-night operation [13]. The model predicts detector dark currents, photocurrents, and readout and background noise associated with a novel small pixel, low-cost SiGe visible-NIR prototype camera. This type of imager, based on the ability to grow NIR-sensitive SiGe layers on silicon to form pixels utilizing existing high quality and low-cost semiconductor and electronic architectures, is intended to provide NIR night vision

A fairly large matrix of variables, which include NIR background, pixel size, focal length, *f*number, integration time, spectral bandpass, dark current level, and readout noise level, require a significantly complex model to perform the necessary design trade studies. This model predicts values for sensor noise equivalent intensity (NEI) and SNR, and also generates simulated 30 and 60 Hz NIR image sequences. The model was designed to assist in the

with NIR FPA manufacturing.

muzzle flash detection [25].

**3.1. Performance model overview**

capability in addition to visible operation.

**3. SiGe sensor performance modeling**

320 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

The NIR background radiance between overcast dark night and full daylight varies by about eight orders of magnitude, spanning approximately 0.1 mlux to 25,000 lux. For daytime operation, spectral filtering, aperture reduction, and/or integration time reduction are required to prevent saturation of an FPA. The night radiance over the visible-NIR wavelength range spanning 400-1750 nm can also be quite varied: ~1.0×10-9 W/cm2 for overcast rural settings, ~1.5×10-9 W/cm2 for overcast urban conditions, ~1.2×10-8 W/cm2 for clear night sky rural conditions, and up to ~3.1×10-8 W/cm2 for clear moonlit night skies. conditions or under a thick canopy. Moonlight and light pollution that exist in more urban settings can also help to illuminate terrain, but such illumination occurs mostly at shorter wavelengths. This situation is shown in Figure 4 in which the lunar radiance is mainly significant in the 400-1200 nm region, and is particularly evident in Figure 4(c) which shows the effects of city light pollution (where the radiance level is derived from a Toronto, Canada based spectral measurement). These spectral radiances have been modeled in order to determine the electron noise level in NIR FPAs for a given FPA pixel size, spectral band, integration time, and set of optics. This provides the background limited performance (BLIP) conditions to which

**Figure 4.** Visible to NIR spectral radiance of night sky based on astronomical data [27] along with data from M. Vatsia [28] plotted in (a), and data from R. Littleton [29] plotted in (b); in (c), radiance includes light pollution (Toronto). In these plots, airglow is shown in orange, moonlight in white, zodiacal IR in beige, **Figure 4.** Visible to NIR spectral radiance of night sky based on astronomical data [27] along with data from M. Vatsia [28] plotted in (a), and data from R. Littleton [29] plotted in (b); in (c), radiance includes light pollution (Toronto). In these plots, airglow is shown in orange, moonlight in white, zodiacal IR in beige, lower atmosphere radiance in light blue, total radiance transmitted to ground in black, and total radiance to ground from airglow alone in dark blue.

lower atmosphere radiance in light blue, total radiance transmitted to ground in

black, and total radiance to ground from airglow alone in dark blue.

7

Since the primary source of illumination in the NIR regime is upper atmosphere airglow, the imaging performance NIR cameras typically degrades when used in dark night overcast conditions or under a thick canopy. Moonlight and light pollution that exist in more urban settings can also help to illuminate terrain, but such illumination occurs mostly at shorter wavelengths. This situation is shown in Figure 4 in which the lunar radiance is mainly significant in the 400-1200 nm region, and is particularly evident in Figure 4(c) which shows the effects of city light pollution (where the radiance level is derived from a Toronto, Canada based spectral measurement). These spectral radiances have been modeled in order to determine the electron noise level in NIR FPAs for a given FPA pixel size, spectral band, integration time, and set of optics. This provides the background limited performance (BLIP) conditions to which dark currents and the readout noise must be added. **Figure 4.** Visible to NIR spectral radiance of night sky based on astronomical data [27] along with data from M. Vatsia [28] plotted in (a), and data from R. Littleton [29] plotted in (b); in (c), radiance includes light pollution (Toronto). In these plots, airglow is shown in orange, moonlight in white, zodiacal IR in beige, lower atmosphere radiance in light blue, total radiance transmitted to ground in black, and total radiance to ground from airglow alone in dark blue.

Basic atmospheric transmittance and path radiance capabilities have been included in the model. The percent cloud cover, which attenuates the airglow and celestial sources as well as the specified solar scattering level, can be taken into account along with aerosol visibility (5 km or 23 km). The transmittance from scene to sensor assumes a horizontal path at the earth's surface. The attenuation effects of the atmosphere on the images were computed, and subse‐ quently a path radiance based on the ambient NIR background was reinserted into the images. This effectively compensated for the loss of scene brightness and contrast with attenuation and the overall increase in brightness due to path radiance. The images in Figure 5 illustrate the loss of contrast with increasing range. Basic atmospheric transmittance and path radiance capabilities have been included in the model. The percent cloud cover, which attenuates the airglow and celestial sources as well as the specified solar scattering level, can be taken into account along with aerosol visibility (5 km or 23 km). The transmittance from scene to sensor assumes a horizontal path at the earth's surface. The attenuation effects of the atmosphere on the images were computed, and subsequently a path radiance based on the ambient NIR background was reinserted into the images. This effectively compensated for the loss of scene brightness and contrast with attenuation and the overall increase in brightness due to path radiance. The images in Figure 5 illustrate the loss of contrast with increasing range.

**Figure 5.** Atmospheric effects on clear night sky. NIR images at distances of 1, 10, and 15 km (left to right) for 5 km visibility conditions. **Figure 5.** Atmospheric effects on clear night sky. NIR images at distances of 1, 10, and 15 km (left to right) for 5 km visibility conditions.

#### **3.3 Image Quality Metrics 3.3. Image quality metrics**

8

Figure 6 displays images from a simulated camera to illustrate the effects of resolution and SNR on image quality and potential image identification. For 30 or 60 Hz image sequences, the eye can integrate some of the frames which allows for slightly better identification than is seen in these single images. Motion of an object over the field-of-view also aids in identification, since Figure 6 displays images from a simulated camera to illustrate the effects of resolution and SNR on image quality and potential image identification. For 30 or 60 Hz image sequences, the eye can integrate some of the frames which allows for slightly better identification than is seen in these single images. Motion of an object over the field-of-view also aids in identification, since the eye can compensate for pixilation when viewing a moving object.

the eye can compensate for pixilation when viewing a moving object.

**Figure 6.** Effects of SNR and resolution on imagery; middle column is typical of **Figure 6.** Effects of SNR and resolution on imagery; middle column is typical of an *f*/1.5, 60 Hz, 15 μm pixel broadband NIR imager. The rows (top to bottom) show reduction in resolution (1X, 2X, and 4X). The columns (left to right) show no noise, SNR=3.5 or NEI=2.2×1010 photons/s-cm2 , and SNR=1 or NEI=7.7×1010 photons/s-cm2 .

an *f*/1.5, 60 Hz, 15 µm pixel broadband NIR imager. The rows (top to bottom)

, and SNR = 1 or NEI =

#### show reduction in resolution (1X, 2X, and 4X). The columns (left to right) show no noise, SNR = 3.5 or NEI = 2.2×1010 photons/s-cm2 **3.4. Maximizing the signal**

9

Since the primary source of illumination in the NIR regime is upper atmosphere airglow, the imaging performance NIR cameras typically degrades when used in dark night overcast conditions or under a thick canopy. Moonlight and light pollution that exist in more urban settings can also help to illuminate terrain, but such illumination occurs mostly at shorter wavelengths. This situation is shown in Figure 4 in which the lunar radiance is mainly significant in the 400-1200 nm region, and is particularly evident in Figure 4(c) which shows the effects of city light pollution (where the radiance level is derived from a Toronto, Canada based spectral measurement). These spectral radiances have been modeled in order to determine the electron noise level in NIR FPAs for a given FPA pixel size, spectral band, integration time, and set of optics. This provides the background limited performance (BLIP)

**Figure 4.** Visible to NIR spectral radiance of night sky based on astronomical data [27] along with data from M. Vatsia [28] plotted in (a), and data from R. Littleton [29] plotted in (b); in (c), radiance includes light pollution (Toronto). In these plots, airglow is shown in orange, moonlight in white, zodiacal IR in beige, lower atmosphere radiance in light blue, total radiance transmitted to ground in

Basic atmospheric transmittance and path radiance capabilities have been included in the model. The percent cloud cover, which attenuates the airglow and celestial sources as well as the specified solar scattering level, can be taken into account along with aerosol visibility (5 km or 23 km). The transmittance from scene to sensor assumes a horizontal path at the earth's surface. The attenuation effects of the atmosphere on the images were computed, and subse‐ quently a path radiance based on the ambient NIR background was reinserted into the images. This effectively compensated for the loss of scene brightness and contrast with attenuation and the overall increase in brightness due to path radiance. The images in Figure 5 illustrate the

Basic atmospheric transmittance and path radiance capabilities have been included in the model. The percent cloud cover, which attenuates the airglow and celestial sources as well as the specified solar scattering level, can be taken into account along with aerosol visibility (5 km or 23 km). The transmittance from scene to sensor assumes a horizontal path at the earth's surface. The attenuation effects of the atmosphere on the images were computed, and subsequently a path radiance based on the ambient NIR background was reinserted into the images. This effectively compensated for the loss of scene brightness and contrast with attenuation and the overall increase in brightness due to path radiance. The images in Figure 5 illustrate the loss of contrast

50 100 150 200 250 300

**Figure 5.** Atmospheric effects on clear night sky. NIR images at distances of 1,

**Figure 5.** Atmospheric effects on clear night sky. NIR images at distances of 1, 10, and 15 km (left to right) for 5 km

Figure 6 displays images from a simulated camera to illustrate the effects of resolution and SNR on image quality and potential image identification. For 30 or 60 Hz image sequences, the eye can integrate some of the frames which allows for slightly better identification than is seen in these single images. Motion of an object over the field-of-view also aids in identification, since

Figure 6 displays images from a simulated camera to illustrate the effects of resolution and SNR on image quality and potential image identification. For 30 or 60 Hz image sequences, the eye can integrate some of the frames which allows for slightly better identification than is seen in these single images. Motion of an object over the field-of-view also aids in identification,

50 100 150 200 250 300

conditions to which dark currents and the readout noise must be added.

322 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

10, and 15 km (left to right) for 5 km visibility conditions.

the eye can compensate for pixilation when viewing a moving object.

since the eye can compensate for pixilation when viewing a moving object.

black, and total radiance to ground from airglow alone in dark blue.

loss of contrast with increasing range.

50 100 150 200 250 300

**3.3 Image Quality Metrics** 

**3.3. Image quality metrics**

visibility conditions.

with increasing range.

8

7.7×1010 photons/s-cm2 . **3.4 Maximizing the Signal**  The available signal is determined based on the FPA integration time, quantum efficiency (QE), optics *f*-number (defined as the ratio of lens focal length to diameter of the entrance pupil), and visible-NIR background in the chosen spectral band. The general SNR is calculated as [13]:

The available signal is determined based on the FPA integration time, quantum efficiency (QE), optics *f*-number (defined as the ratio of lens focal length to diameter of the entrance pupil), and visible-NIR background in the chosen spectral band. The general SNR is calculated as [13]:

$$\text{SNNR} = \frac{e\_{sig}}{\tilde{e}\_{noise}} = \frac{e\_{bk,NIR}}{\sqrt{e\_{n,bk}^2 + e\_{n,real}^2 + e\_{n,dark}^2}} \tag{1}$$

where the noise level consists of background, read, and dark current noise. The signal as measured by collected electrons *e*sig is given by

$$\sigma\_{\rm sig} = t\_i G \tau\_o f \eta \frac{A\_{\rm det}}{4F\_\#^2} \int\_{\lambda\_1}^{\lambda\_2} \Phi\_{bk} d\lambda \tag{2}$$

where *t*<sup>i</sup> is the integration time, *G* is the gain, *τ*<sup>o</sup> is the optics transmittance, *f* is the fill factor, *η* is the QE, *A*det is the detector area, *F*# is the *f*-number, and Φbk is the visible-NIR background in photons/sec-cm2 . The background consists of airglow, moonlight and light pollution sources:

$$\int\_{\lambda\_1}^{\lambda\_2} \Phi\_{bk} d\lambda = \int\_{\lambda\_1}^{\lambda\_2} \left[ t\_a \left( \Phi\_{a \text{ir} \text{g} \text{low}} + \Phi\_{m \text{on}} + \Phi\_{\text{solar}} \right) + \Phi\_{\text{light}} \right] d\lambda \tag{3}$$

where the transmittance *τ*a occurs from ground to space.

#### **3.5. Minimizing noise**

The NIR camera noise is a combination of the background noise, readout noise (typically consisting of a few electrons to tens of electrons), and dark current noise. In designing the optics and setting the parameters of the FPA, the dark current and readout noise must be maintained below the background noise. The *f*-number is the metric for signal and background level noise; however, the focal length required for identifying the object of interest at the desired range must first be specified before the *f*-number can be determined. It is necessary to know the focal length along with the *f*-number in order to obtain an adequately accurate SNR for the specific night sky background, which in turn is used to determine the required optical aperture.

The readout noise *e*n,read is normally in the range of 10-50 electrons. The background noise is simply the square root of the background electrons collected:

$$e\_{n,bk} = \sqrt{t\_i G \tau\_o f \eta \frac{A\_{det}}{4F\_\sharp^2} \int\_{\lambda\_1}^{\lambda\_2} \Phi\_{bk} d\lambda} \tag{4}$$

Likewise, the dark current noise may be expressed as

SiGe Based Visible-NIR Photodetector Technology for Optoelectronic Applications http://dx.doi.org/10.5772/59065 325

$$e\_{n,dark} = \sqrt{\frac{t\_i G I\_{dark}}{q}} = \sqrt{\frac{t\_i G I\_{dark} A\_{det}}{q}} \tag{5}$$

If the dark current, which is a function of the bias voltage, is further reduced by decreasing the negative bias, uniformity and responsivity may be degraded.

= =

324 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

measured by collected electrons *e*sig is given by

photons/sec-cm2

**3.5. Minimizing noise**

aperture.

l

Fl

l

 l

> F

 l

where the transmittance *τ*a occurs from ground to space.

simply the square root of the background electrons collected:

Likewise, the dark current noise may be expressed as

SNR *sig bk,NIR*

*e e*

 = th

*<sup>A</sup> e tG f <sup>d</sup>*

+ + % 22 2

*e ee e*

*noise n,bk n,read n,dark*

where the noise level consists of background, read, and dark current noise. The signal as

l

 F lò <sup>2</sup>

. The background consists of airglow, moonlight and light pollution sources:

1 1 *bk a airglow moon solar lightpol d t <sup>d</sup>* (3)

 F

*<sup>F</sup>* (2)

 l

*<sup>F</sup>* (4)

l

<sup>1</sup> <sup>2</sup> 4 *det sig i o bk #*

where *t*<sup>i</sup> is the integration time, *G* is the gain, *τ*<sup>o</sup> is the optics transmittance, *f* is the fill factor, *η* is the QE, *A*det is the detector area, *F*# is the *f*-number, and Φbk is the visible-NIR background in

( )

= ++ + é ù

The NIR camera noise is a combination of the background noise, readout noise (typically consisting of a few electrons to tens of electrons), and dark current noise. In designing the optics and setting the parameters of the FPA, the dark current and readout noise must be maintained below the background noise. The *f*-number is the metric for signal and background level noise; however, the focal length required for identifying the object of interest at the desired range must first be specified before the *f*-number can be determined. It is necessary to know the focal length along with the *f*-number in order to obtain an adequately accurate SNR for the specific night sky background, which in turn is used to determine the required optical

The readout noise *e*n,read is normally in the range of 10-50 electrons. The background noise is

 = th

*n,bk i o bk*

*<sup>A</sup> e tG f <sup>d</sup>*

l

 F lò <sup>2</sup>

l

<sup>1</sup> <sup>2</sup> 4 *det*

*#*

 F

 F

ë û ò ò 2 2

(1)

In addition to these basic temporal noises, NIR cameras exhibit spatial noise. Although calibrations usually reduce the spatial noise to levels below that of the temporal noise, spatial noise varieties such as random pattern noise, fixed row and column noise, temporal row and column noise, and frame fluctuation noise all can be observed in the images. The model incorporates all the noise types described in a three-dimensional (3D) noise model, the concept of which is illustrated in Figure 7.

**Figure 7.** Method of deriving 3D noise from the model illustrated.

The background SNR formula for specific dependencies is expressed as

$$\text{SNR}\_{bk} = \sqrt{t\_i G \tau\_o f \eta \frac{A\_{det}}{4F\_\sharp^2} \int\_{\lambda\_1}^{\lambda\_2} \Phi\_{bk} d\lambda} \tag{6}$$

while the dark current SNR is given by the formula

$$\text{SNR}\_{dark} = \frac{\sqrt{q t\_i G A\_{det}} \tau\_o f \eta}{4 F\_\#^2 \sqrt{J\_{dark}}} \int\_{\lambda\_1}^{\lambda\_2} \Phi\_{\text{bk}} d\lambda \tag{7}$$

The sensor NEI condition is

$$\int\_{\lambda\_1}^{\lambda\_2} \Phi\_{bk} d\lambda = NEI = \frac{\sqrt{e\_{n,real}^2 + e\_{n,bk}^2 + e\_{n,dark}^2}}{t\_i G \tau\_o f \eta \frac{A\_{det}}{4F\_\sharp^2}}\tag{8}$$

Typical NEIs are in the 8×108 to 5×109 photon/s-cm2 range and vary with integration time and *f*-number, where nominal values are in the ranges of 16 to 33 ms and *f*/1.0 to *f*/1.5, respectively. The SNRs in view are for single frames. As was noted, ability of the human eye/brain to integrate some of the frames when perceiving 30 to 60 Hz imagery improves detection and identification performance compared to single static frame viewing. The improvement for random temporal noise dominated images generally varies with the square root of the number of frames the eye can integrate. Eye integration is complicated and varies with light level, resolution, and other factors. This improvement is not only limited by the temporal duration of the eye integration, but also by the underlying spatial noise of the sensor image. Since the level of spatial noise including row and column noise is often marginally below the level of the temporal noise, the eye integration improvement ceases when temporal noise abatement becomes equal to the spatial noise.

The SNR can also be improved by spatially binning pixels, but this is at the expense of sacrificing spatial resolution. This SNR improvement is generally proportional to the square root of the number of binned pixels. Thus, implementing 2×2 binning improves the SNR by a factor of 2. Adding these two phenomena to the previously derived SNR gives:

$$\text{SNR} = \frac{\varepsilon\_{\text{sig}}}{\tilde{\varepsilon}\_{\text{noise}}} = \frac{\varepsilon\_{bk,\text{svir}} N\_{\text{fs}} N\_{\text{ps}}}{\sqrt{N\_{\text{fs}} N\_{\text{ps}} \|\varepsilon\_{n,\text{bk}}^2 + \varepsilon\_{n,\text{rad}}^2 + \varepsilon\_{n,\text{drck}}^2 \|\_{\text{temporal}} + N\_{\text{fs}} N\_{\text{ps}} \varepsilon\_{n,\text{spatial}}}} \tag{9}$$

This expression shows the improvement in SNR with the square root of the product of summed pixels and summed frames for the temporal noise part, and demonstrates the ineffectiveness of summing toward improving the SNR of spatial noise dominated imagery.

### **3.6. Predicting NEI and SNR**

The background SNR formula for specific dependencies is expressed as

326 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

while the dark current SNR is given by the formula

l

F l

*bk*

to 5×109

l

1

The sensor NEI condition is

Typical NEIs are in the 8×108

becomes equal to the spatial noise.

= =

*SNR*

 = th

=

+ + = = <sup>ò</sup> <sup>2</sup>

*d NEI <sup>A</sup> tG f <sup>F</sup>*

*<sup>A</sup> SNR t G f <sup>d</sup>*

l

 F lò <sup>2</sup>

l

F lò <sup>2</sup>

l

t h

*i o*

*f*-number, where nominal values are in the ranges of 16 to 33 ms and *f*/1.0 to *f*/1.5, respectively. The SNRs in view are for single frames. As was noted, ability of the human eye/brain to integrate some of the frames when perceiving 30 to 60 Hz imagery improves detection and identification performance compared to single static frame viewing. The improvement for random temporal noise dominated images generally varies with the square root of the number of frames the eye can integrate. Eye integration is complicated and varies with light level, resolution, and other factors. This improvement is not only limited by the temporal duration of the eye integration, but also by the underlying spatial noise of the sensor image. Since the level of spatial noise including row and column noise is often marginally below the level of the temporal noise, the eye integration improvement ceases when temporal noise abatement

The SNR can also be improved by spatially binning pixels, but this is at the expense of sacrificing spatial resolution. This SNR improvement is generally proportional to the square root of the number of binned pixels. Thus, implementing 2×2 binning improves the SNR by a

*noise fs ps n,bk n,read n,dark temporal fs ps n,spatial*

*<sup>e</sup> N N [e e e ] N N e* (9)

factor of 2. Adding these two phenomena to the previously derived SNR gives:

++ + % 22 2 *sig bk,swir fs ps*

*e e NN*

2 22

*e ee*

*n,read n,bk n,dark*

<sup>2</sup> 4

*det*

*#*

*<sup>F</sup>* (6)

*F J* (7)

photon/s-cm2 range and vary with integration time and

(8)

l

<sup>1</sup> <sup>2</sup> 4 *det bk i o bk #*

> t h

<sup>1</sup> <sup>2</sup> 4 *i det o dark bk # dark qt GA f SNR <sup>d</sup>*

NEI vs. operating temperature for pixel sizes of 30, 20, 10 and 5 μm is shown plotted in Figure 8 using a diffusion expression derived from low dark current density data. For these simula‐ tions, the following parameters were employed: integration time of 33 ms, gain of unity, read noise of 10 electrons rms, dark current residual nonuniformity calculated for a temperature delta of 0.1 K, optics with *f*/1.25, QE of 80%, and wavelength range spanning 1000-1750 nm. It canbeseenthattheNEIduetodarkcurrent(bluesquares)increasesas thepixel sizeisdecreased, since the dark current noise is a function of linear pixel size while light collection is a function ofpixelarea.TheNEIimproveswithpixelsizebecausethenumberofphotonscollectedincreases with detector area while the BLIP noise increases in proportion to the square root ofthe detector area.Forthe sensormodeled,theBLIPNEIfor 30μmpixels is 1.5×109photons/s-cm2 , significant‐ ly lower than the value of 9×109 photons/s-cm2 determined for 5 μm pixels.

**Figure 8.** NEI vs. operating temperature for visible-NIR sensors with various pixel sizes: (a) 30 µm, (b) 20 µm, (c) 10 µm, and (d) 5 µm. Minimizing dark current in SiGe detectors, especially for those with smaller pixels, is a driving **Figure 8.** NEI vs. operating temperature for visible-NIR sensors with various pixel sizes: (a) 30 μm, (b) 20 μm, (c) 10 μm, and (d) 5 μm.

requirement. Figure 9 shows the SNR vs. dark current density for 7.5 and 12 µm pixels as a function of dark current density. The level lines are the readout and background SNRs and the slanted lines are the dark current SNRs. The background SNR is the best attainable SNR. The intersection of the lines thus signifies the dark current level where the dark current SNR is equal to the readout or background SNR. In Figure 9(a), the yellow lines signify the background or BLIP SNRs for clear skies with no moonlight for the two pixel sizes, with the upper yellow line showing the SNR for 12 µm pixels and 0.89 moonlight conditions. In Figure 9(b), the readout noise SNR (red squares) has been added for both large and small pixels (based on 10 noise

13

electrons per integration).

Minimizing dark current in SiGe detectors, especially for those with smaller pixels, is a driving requirement. Figure 9 shows the SNR vs. dark current density for 7.5 and 12 μm pixels as a function of dark current density. The level lines are the readout and background SNRs and the slanted lines are the dark current SNRs. The background SNR is the best attainable SNR. The intersection of the lines thus signifies the dark current level where the dark current SNR is equal to the readout or background SNR. In Figure 9(a), the yellow lines signify the back‐ ground or BLIP SNRs for clear skies with no moonlight for the two pixel sizes, with the upper yellow line showing the SNR for 12 μm pixels and 0.89 moonlight conditions. In Figure 9(b), the readout noise SNR (red squares) has been added for both large and small pixels (based on 10 noise electrons per integration).

**Figure 9.** (a) SNR vs. dark current density for 7.5 and 12 µm pixels for dark sky, 0.89 moonlight conditions, *f*/1.25, 33 ms integration time, and 400-1750 nm bandpass; (b) shows the addition of read noise based SNR (10 electrons). **Figure 9.** (a) SNR vs. dark current density for 7.5 and 12 μm pixels for dark sky, 0.89 moonlight conditions, *f*/1.25, 33 ms integration time, and 400-1750 nm bandpass; (b) shows the addition of read noise based SNR (10 electrons).

Dark current appears to be the performance limiting factor for small pixel NIR FPAs operating at RT. The performance can be improved by compensating for the dark currents using lookup tables, though nonuniformity due to uncompensated variance in dark current over the FPA must also be characterized. While utilizing lookup tables should smooth out most of the nonuniformity, there will be residual nonuniformity as a result of the FPA pixels' dark current to temperature difference ratios at RT in combination with the temperature increment used in the lookup tables. The dark current residual nonuniformity must be kept below the average dark current noise level to preserve the performance, as illustrated in Figure 9. **3.7 SiGe Imager Performance Based on Modeling Results**  Dark current appears to be the performance limiting factor for small pixel NIR FPAs operating at RT. The performance can be improved by compensating for the dark currents using lookup tables, though nonuniformity due to uncompensated variance in dark current over the FPA must also be characterized. While utilizing lookup tables should smooth out most of the nonuniformity, there will be residual nonuniformity as a result of the FPA pixels' dark current to temperature difference ratios at RT in combination with the temperature increment used in the lookup tables. The dark current residual nonuniformity must be kept below the average dark current noise level to preserve the performance, as illustrated in Figure 9.

#### Miniature SiGe detector based FPAs that can be incorporated into handheld cameras or inserted **3.7. SiGe imager performance based on modeling results**

into smartphones require *f*/2 to *f*/3 optics and pixels approximately 5-7 µm in size. These detectors will consequently have reduced light collection with relatively high dark currents at RT. Such higher *f*-numbers, which are about twice those characteristic of an ideal NIR camera, effectively reduce the signal and SNR by about a factor of four. While small optics of *f*/1 to *f*/1.5 are possible, these may require an increase in optics diameter. Another method to improve the SNR in dark current limited NIR sensors is to incorporate a microlens array (e.g., having 20 µm lens centers) to focus light from the scene onto 5-7 *µ*m detector pixels. This maintains the signal strength while reducing detector dark current, enabling small pixel sizes within a larger cell that allows for extra on-chip signal processing electronics. Miniature SiGe detector based FPAs that can be incorporated into handheld cameras or inserted into smartphones require *f*/2 to *f*/3 optics and pixels approximately 5-7 μm in size. These detectors will consequently have reduced light collection with relatively high dark currents at RT. Such higher *f*-numbers, which are about twice those characteristic of an ideal NIR camera, effectively reduce the signal and SNR by about a factor of four. While small optics of *f*/1 to *f*/1.5 are possible, these may require an increase in optics diameter. Another method

Predictions based on the modeling that has been detailed in this section are summarized as follows: Imaging under rural night sky conditions becomes challenging for small pixel, small optics designs, and dark currents can significantly impact performance in an uncooled NIR camera. A small NIR camera will respond well to minimal amounts of illumination from a direct

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to improve the SNR in dark current limited NIR sensors is to incorporate a microlens array (e.g., having 20 μm lens centers) to focus light from the scene onto 5-7 *µ*m detector pixels. This maintains the signal strength while reducing detector dark current, enabling small pixel sizes within a larger cell that allows for extra on-chip signal processing electronics.

Predictions based on the modeling that has been detailed in this section are summarized as follows: Imaging under rural night sky conditions becomes challenging for small pixel, small optics designs, and dark currents can significantly impact performance in an uncooled NIR camera. A small NIR camera will respond well to minimal amounts of illumination from a direct NIR source, such as one imaged in indoor or shorter-range outdoor environments. In addition, the performance limitations of small uncooled NIR cameras are not found to be problematic for live fire detection and identification applications. Overall, these findings indicate that low-cost, small pixel, uncooled detectors based on growth of SiGe on Si are potentially advantageous for imaging in indoor or low light level outdoor environments.
