Within a pixel in a digital imager, generally either a charge-coupled device or complementary metal oxide semiconductor device, doping of the semiconductor substrate and application of gate voltages create a region free of mobile carriers called the depletion region. This region fills with charge after incoming photons or thermal energy raise the charges from the valence to the conduction energy band. As the signal charge fills the depletion region, the electric field generating the region is altered, and the size of the region is reduced. We present a model that describes how this dynamic depletion region, along with the location of impurities, will result in pixels that produce less dark current after being exposed to light and additionally show nonlinear production rates with respect to exposure time. These types of effects have been observed in digital imagers, allowing us to compare empirical data with the modeled data.
KEYWORDS: Data modeling, Imaging systems, Charge-coupled devices, 3D modeling, Cameras, Systems modeling, Oxides, CCD image sensors, Electrons, Camera shutters
The depletion edge in Charge-Coupled Devices (CCD) pixels is dependent upon the amount of signal charge located
within the depletion region. A model is presented that describes the movement of the depletion edge with increasing
signal charge. This dynamic depletion edge is shown to have an effect on the amount of dark current produced by some
pixels. Modeling the dark current behavior of pixels both with and without impurities over an entire imager demonstrates
that this moving depletion edge has a significant effect on a subset of the pixels. Dark current collected by these pixels is
shown to behave nonlinearly with respect to exposure time and additionally the dark current is affected by the presence
of illumination. The model successfully predicts unexplained aspects of dark current behavior previously observed in
some CCD sensors.
It is generally assumed that charge-coupled device (CCD) imagers produce a linear response of dark current versus
exposure time except near saturation. We found a large number of pixels with nonlinear dark current response to
exposure time to be present in two scientific CCD imagers. These pixels are found to exhibit distinguishable behavior
with other analogous pixels and therefore can be characterized in groupings. Data from two Kodak CCD sensors are
presented for exposure times from a few seconds up to two hours. Linear behavior is traditionally taken for granted when
carrying out dark current correction and as a result, pixels with nonlinear behavior will be corrected inaccurately.
We present an analysis of dark current from a complementary metal-oxide-semiconductor (CMOS) active pixels sensor with global shutter. The presence of two sources of dark current, one within the collection area of the pixel and another within the sense node, present complications to correction of the dark current. The two sources are shown to generate unique and characteristic dark current behavior with respect to varying exposure time, temperature, and/or frame rate. In particular, a pixel with storage time in the sense node will show a dark current dependence on frame rate and the appearance of being a "stuck pixel" with values independent of exposure time. On the other hand, a pixel with an impurity located within the collection area will show no frame rate dependence, but rather a linear dependence on exposure time. A method of computing dark frames based on past dark current behavior of the sensor is presented and shown to intrinsically compensate for the two different and unique sources. In addition, dark frames requiring subtraction of negative values, arising from the option to modify the bias offset, are shown to be appropriate and possible using the computational method.
KEYWORDS: Diffusion, Charge-coupled devices, Electrons, Data modeling, Monte Carlo methods, Back illuminated sensors, Sensors, Optical engineering, Spatial resolution, Absorption
The potential well in back-illuminated charge-coupled devices (CCDs) does not reach all the way to the back surface. Hence, light that is absorbed in the field-free region generates electrons that can diffuse into neighboring pixels and thus decreases the spatial resolution of the sensor. We present data for the charge diffusion from a near point source by measuring the response of a back-illuminated CCD to light emitted from a submicron diameter glass fiber tip. The diffusion of electrons into neighboring pixels is analyzed for different wavelengths of light ranging from 430 to 780 nm. To find out how the charge spreading into other pixels depends on the location of the light spot; the fiber tip could be moved with a piezoelectric translation stage. The experimental data are compared to Monte Carlo simulations and an analytical model of electron diffusion in the field-free region. The presented analysis can be used to predict the charge diffusion in other back-illuminated sensors, and the experiment is universally applicable to measure any type of sensors.
A study of dark current in digital imagers within consumer grade digital cameras is presented. Dark current is shown
to vary with temperature, exposure time, and ISO setting. Further, dark current is shown to increase in successive
images during a series of images. Consumer cameras are often designed to be as compact as possible and therefore
the digital imagers within the camera frame are prone to heat generated by nearby elements within the camera body.
It is the scope of this work to characterize the dark current in such cameras and to show that the dark current, in part
due to heat generated by the camera itself, can be corrected for by using hot pixels on the imager. This method
generates computed dark frames based on the dark current indicator value of the hottest pixels on the chip. We
compare this method to standard methods of dark current correction.
A study of dark current in digital imagers in digital single-lens reflex (DSLR) and compact consumer-grade digital cameras is presented. Dark current is shown to vary with temperature, exposure time, and ISO setting. Further, dark current is shown to increase in successive images during a series of images. DSLR and compact consumer cameras are often designed such that they are contained within a densely packed camera body, and therefore the digital imagers within the camera frame are prone to heat generated by the sensor as well as nearby elements within the camera body. It is the scope of this work to characterize the dark current in such cameras and to show that the dark current, in part due to heat generated by the camera itself, can be corrected by using hot pixels on the imager. This method generates computed dark frames based on the dark current indicator value of the hottest pixels on the chip. We compare this method to standard methods of dark current correction.
Thermal excitation of electrons is a major source of noise in charge-coupled-device (CCD) imagers. Those electrons are generated even in the absence of light, hence, the name dark current. Dark current is particularly important for long exposure times and elevated temperatures. The standard procedure to correct for dark current is to take several pictures under the same condition as the real image, except with the shutter closed. The resulting dark frame is later subtracted from the exposed image. We address the question of whether the dark current produced in an image taken with a closed shutter is identical to the dark current produced in an exposure in the presence of light. In our investigation, we illuminated two different CCD chips with different intensities of light and measured the dark current generation. A surprising result of this study is that some pixels produce a different amount of dark current under illumination. Finally, we discuss the implication of this finding for dark frame image correction.
Digital single-lens reflex (DSLR) cameras are examined and their dark current behavior is presented. We examine the
influence of varying temperature, exposure time, and gain setting on dark current. Dark current behavior unique to
sensors within such cameras is observed. In particular, heat is trapped within the camera body resulting in higher
internal temperatures and an increase in dark current after successive images. We look at the possibility of correcting for
the dark current, based on previous work done for scientific grade imagers, where hot pixels are used as indicators for
the entire chip's dark current behavior. Standard methods of dark current correction are compared to computed dark
frames. Dark current is a concern for DSLR cameras as optimum conditions for limiting dark current, such as cooling the
imager, are not easily obtained in the typical use of such imagers.
Thermal excitation of electrons is a major source of noise in Charge-Coupled Device (CCD) imagers. Those electrons are generated even in the absence of light, hence the name dark current. Dark current is particularly important for long exposure times and elevated temperatures. The standard procedure to correct for dark current is to take several pictures under the same condition as the real image, except with the shutter closed. The resulting dark frame is later subtracted from the exposed image. We address the question of whether the dark current produced in an image taken with a closed shutter is identical to the dark current produced in an exposure in the presence of light. In our investigation, we illuminated two different CCD chips to different intensities of light and measured the dark current generation. A surprising conclusion of this study is that some pixels produce a different amount of dark current under illumination. Finally, we discuss the implications that this has for dark frame image correction.
We present data for the dark current of a commercially available CMOS image sensor for different gain settings and bias offsets over the temperature range of 295 to 340 K and exposure times of 0 to 500 ms. The analysis of hot pixels shows two different sources of dark current. One source results in hot pixels with high but constant count for exposure times smaller than the frame time. Other hot pixels exhibit a linear increase with exposure time. We discuss how these hot pixels can be used to calculate the dark current for all pixels. Finally, we show that for low bias settings with universally zero counts for the dark frame one still needs to correct for dark current. The correction of thermal noise can therefore result in dark frames with negative pixel values. We show how one can calculate dark frames with negative pixel count.
KEYWORDS: Temperature metrology, Cameras, Imaging systems, Calibration, Electrons, Signal to noise ratio, Temperature sensors, Astronomy, Charge-coupled devices, Control systems
Dark current is caused by electrons that are thermally exited into the conduction band. These electrons are collected by
the well of the CCD and add a false signal to the chip. We will present an algorithm that automatically corrects for dark
current. It uses a calibration protocol to characterize the image sensor for different temperatures. For a given exposure
time, the dark current of every pixel is characteristic of a specific temperature. The dark current of every pixel can
therefore be used as an indicator of the temperature. Hot pixels have the highest signal-to-noise ratio and are the best
temperature sensors. We use the dark current of a several hundred hot pixels to sense the chip temperature and predict
the dark current of all pixels on the chip. Dark current computation is not a new concept, but our approach is unique.
Some advantages of our method include applicability for poorly temperature-controlled camera systems and the
possibility of ex post facto dark current correction.
With a band gap of silicon of 1.1eV, the largest wavelength that can excite electrons from the valence to the conduction band is roughly 1100nm. As a consequence, in, for instance, a charge-coupled device, the quantum efficiency (QE) for wavelengths larger than 1100nm is assumed to be zero. We found that there is a response at those longer wavelengths and that the response decreases with increasing wavelength. The QE increases with increasing chip temperature which suggests a thermally activated process. Impurities in the silicon provide the energy levels in the band gap, from which electrons can be excited either thermally or by absorption of a photon. It is these impurities that contribute to the infrared response. We characterized the response at chip temperatures of 248 K to 293 K for wavelengths from 1200 nm to 1600 nm and calculated the activation energies at these wavelengths. We found that hot pixels, i.e., pixels with extraordinary high counts in a dark frame, tend to respond stronger to infrared light than normal pixels. This correlation gets stronger for longer wavelengths. It is argued that this response can be used for probing the impurities present in the silicon bulk of the sensors.
KEYWORDS: Charge-coupled devices, Diffusion, Electrons, Data modeling, Point spread functions, Back illuminated sensors, Monte Carlo methods, Modulation transfer functions, Spatial resolution, Light sources
The spatial resolution of an optical device is generally characterized by either the Point Spread Function (PSF) or the Modulation Transfer Function (MTF). To directly obtain the PSF one needs to measure the response of an optical system to a point light source. We present data that show the response of a back-illuminated CCD to light emitted from a sub-micron diameter glass fiber tip. The potential well in back-illuminated CCD’s does not reach all the way to the back surface. Hence, light that is absorbed in the field-free region generates electrons that can diffuse into other pixels. We analyzed the diffusion of electrons into neighboring pixels for different wavelengths of light ranging from blue to near infrared. To find out how the charge spreading into other pixels depends on the location of the light spot, the fiber tip could be moved with a piezo-electric translation stage. The experimental data are compared to Monte Carlo simulations and an analytical model of electron diffusion in the field-free region.
We present data for dark current of a back-illuminated CCD over the temperature range of 222 to 291 K. Using an Arrhenius law, we found that the analysis of the data leads to the relation between the prefactor and the apparent activation energy as described by the Meyer-Neldel rule. However, a more detailed analysis shows that the activation energy for the dark current changes in the temperature range investigated. This transition can be explained by the larger relative importance at high temperatures of the diffusion dark current and at low temperatures by the depletion dark current. The diffusion dark current, characterized by the band gap of silicon, is uniform for all pixels. At low temperatures, the depletion dark current, characterized by half the band gap, prevails, but it varies for different pixels. Dark current spikes are pronounced at low temperatures and can be explained by large concentrations of deep level impurities in those particular pixels. We show that fitting the data with the impurity concentration as the only variable can explain the dark current characteristics of all the pixels on the chip.
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