Not necessarily. There are many parameters that go into designing a camera that affect the output number given the same input photons. Each model of camera, even if it uses the same sensor, may have the parameters adjusted differently, resulting in a different output count per detected photon. This ratio of detected photons (photons converted to electrons in each sensor pixel) to the output count is the conversion factor (CF) for the camera, in units of electrons/count and determined by the manufacturer. The conversion factor can also be approximated by the following equation.
The way to compare two cameras is to calculate back to the number of sample photons that the output represents in each case.
The sensor detects photons (P), which are collected as photoelectrons (e-). The number of detected photons depends on the quantum efficiency (QE, in %), which is wavelength dependent, and on the pixel area, which determines how much of the sample emission is covered with each pixel. The photoelectrons are then converted to a voltage in the readout circuit of the sensor. Gain (G), a multiplication factor, may be added before (EM gain) or after (analog gain) the voltage conversion. This voltage goes into a digitizer which outputs a value represented by a whole number, ranging from the digital offset to the maximum value of the digitizer in units of counts. The equation to calculate the input photons from the output counts is derived from going backwards through the process.
If the pixel sizes in the cameras being evaluated are different, then the number of photons per unit should be calculated and compared using the pixel dimensions, photons/µm2.
As an example of comparing two outputs, let’s use one camera that can output the data in either 16-bit or 12-bit format. The conversion factor would be the only parameter that would change between the two modes.
Given a camera with the following specifications:
The conversion factors for 16 and 12 bits are:
Rewriting equation 2 to solve for counts, we get:
We can see that the output in the 16-bit mode is a higher number than the 12-bit mode, but the input number of photons is the same. The 16-bit mode is not detecting more photons than the 12-bit mode.
When comparing image data between two cameras, or even the same camera with different camera settings, it is important to look at the data and think in photons.
InGaAs is an alloy which belongs to the InGaAsP quaternary system that consists of indium arsenide (InAs), gallium arsenide (GaAs), indium phosphide (InP), and gallium phosphide (GaP). These binary materials and their alloys are all III-V compound semiconductors.
The energy bandgap of InGaAs alloys depends on the ratio of indium and gallium content. At room temperature (300 K), the dependency of the energy bandgap on the indium content x (0~1) can be calculated using the formula: Eg(x) = 1.425eV - 1.501eV*x + 0.436eV*x2. The corresponding cutoff wavelength that can be detected is in the range of 870nm~3.4µm.
|Indium Content x||Energy Gap Eg eV||Corresponding Wavelength nm|
The most used substrate for InGaAs is InP. The InGaAs alloy having x=0.530 has the same lattice constant as InP, which is called "standard InGaAs." This combination brings high quality thin films and results in the cutoff wavelength of 1.7µm.
However, many applications require longer wavelengths. Hamamatsu offers both linear and area InGaAs image sensors with cutoff wavelengths up to 2.6µm, which are called “extended wavelength.” Due to the mismatch of the lattice constant of InGaAs and InP, the quality of the thin films is reduced. However, Hamamatsu put in a lot of effort to guarantee top-quality extended InGaAs.
The dark current of Hamamatsu InGaAs image sensors is successfully minimized by operating the photodiode array at zero bias condition. Moreover, one-stage TEC (thermoelectric cooler) or multiple-stage TEC can be added into the sensor package to stabilize the sensor temperature and reduce the dark current efficiently.
Rewording this question into camera terms, we can say, “The input to the camera sensor is blocked from detecting any photons, but the image data on my computer has non-zero values.”
This is an important feature of a scientific digital camera used for quantitative image measurements. To understand why this is the case we need to understand, in very high level terms, the conversion of photons to image data. The sensor detects the photons which are collected as photoelectrons and then passed along as a voltage in the readout circuit of the sensor. This voltage goes into a digitizer, which outputs a value represented by a whole number ranging from 0 to the maximum value of the digitizer. This whole number is referred to as counts, gray values, or gray levels.
The readout of the sensor pixel is an imperfect process and noise is introduced into the signal as it is converted to a voltage reading. This noise is a small fluctuating voltage around the nominal signal. If that signal is 0, then the voltage fluctuates into negative values. Since the digitizer in the camera does not contain values less than zero, these negative voltages would be clipped and data would be lost. To avoid the loss of data, the camera designer will set the zero voltage to be a number higher than zero that will accommodate the noise fluctuation, for example 100 counts on the digitizer. In this case, fluctuations below 0 in voltage would be represented by output counts less than 100 counts.
This non-zero output value for the zero photon input is called the digital offset. The camera manual or camera manufacturer can provide the digital offset number for your camera model. You will need to subtract this digital offset number from each intensity value to determine the true output signal from your camera.
Lu Cheng is an applications engineer, specializing in all of our image sensors and driver circuits. Before joining Hamamatsu, she worked as an analog and mixed-signal ASIC designer. With more than 10 years’ experience in ASIC and circuit board design, she can support you to find the optimized product/solution not only from a user’s perspective but also from a designer’s. Traditional Chinese dancing is one of the things that make her learn about the beauty of the world from a different perspective.
Shelley Brankner is an Applications Engineer specializing in scientific cameras and x-ray imaging products. For customers that need high-level synchronization between their camera and peripheral devices, she can provide the expertise on timing and modes of operation in these imaging products. She has a passion for asking the question, “How does that work?” and a desire for sharing the answer with others. When she isn’t knocking down the technical questions that cross her path, she can be found knocking down pins at a bowling alley.
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