Introduction to CCD/CMOS Detector Calibration



Introduction to CCD/CMOS Detector CalibrationIn this lab we will look at the methods used to calibrate various characteristics common to both CCD and CMOS detectors. Some of the basic properties will measure are the read noise, bias, dark current, gain, and responsivity of the detector. We will discuss each of these in more detail. Please take the time to look over the following links to familiarize yourself with the architecture of both the CCD and CMOS detectors as well as some of their common advantages and disadvantages. Keep these in mind as you are going through the lab to understand how these might be affecting the quantities you are measuring.Optional Preparation ReadingsDigital Imaging – Although focused on CCDs, many of the concepts found here apply to both CCD and CMOS detectors. Reading here is not required, but feel free to glance through to get a primer on many of the topics we will talk D Background InfoCCD Overview – A fairly concise and comprehensive overview of CCD architecture and read outCCD Blooming – A discussion of one of the main challenges in CCD imagingCMOS Background InfoCMOS Overview – From the same company as the CCD OverviewRolling Shutter – An informal discussion of rolling shutters - one of the main challenges of CMOS imaging N.B. The shutter on our CMOS detector actually reads out from the center of the detector, not from top to bottom like animations in the link. This is because it is actually a combination of two separate chips that are read out together. Keep this in mind when going through the lab.GoalsThe goals of this lab are to understand and measure the characteristics of a CMOSCCD detector and how these characteristics may affect the science data we are looking to interpret. As you should have learned from the background readings, a CMOS CCD detector is very similar to a CMOSCD, and although we will focus on characterizing properties common to both detectors, there are some differences between them that will affect our calibration processing (for example, the CMOS’ spatial variability). must be calibrated differently (ex blooming). This lab will have a strong focus on array manipulation and operations as well as statistical fitting and error analysis (it is always important to know the error in any measured quantity). Although this lab will focus on calibrating a CMOS detector, you should think about how a CCD would be calibrated similarly/differently along the way.LogisticsAll of the data you will need to carry out at the can be found in the DATA subdirectory of the LAB2 folder that you downloaded. Also in that directory is a README file that explains the naming conventions for the files as well as the subdirectories included in the download. READ THIS FILE AND BE FAMILIAR WITH THE NAMING CONVENTIONS. Having clear and explicit file names allows for easy automation and processing of the large number of files that we will be working with by pulling all of the necessary information of how the data was collected from the file name.The structure of each section will be an introduction explaining the characteristic of interest followed by a section detailing how to collect the data (all of which will be provided in this case) as well as a guideline to the steps of how to analyze the data. This lab will require much more independent programming than Lab 1 so please feel free to ask any questions to have along the way. As a guideline and tool, a Python script that runs many of the algorithms we will discuss in this lab has been provided. This is meant simply as a helpful hint file. Python handles data differently than Matlab and the script performs functions that are not asked for in this lab – so do not attempt to simply copy functions from the Python file. They will most likely not work for our purposes. Also in each section are questions that have been colored and italicized that should be answered. Like with Lab 1, a separate lab write-up document has been provided (in the REPORT subdirectory) with a copy of all the questions. The questions are included in the lab simply so you can think about them along the way.Please make sure that all plots and images have appropriate titles, legends, colorbars, axis labels, etc. as needed. Anyd unclear or unlabeled plots will not receive full credit. The submission procedure will be the same as for Lab 1 and is detailed in the lab write-up document.Brief Digression: FiltersNeutral Density FiltersBecause the light source we will be using is so bright (even at the lowest levels) we need to use neutral density filters to block a significant fraction of the light reaching the detector. Neutral density filters reduce light equally by a fixed amount across a defined region of wavelengths (for us that region is the optical). They are “neutral” because of this equal reduction. An ND filter is defined by the optical density, τ, given by:IIo=10-τWe will use a combination of τ=.3, .6, & .9 to reduce our light by ~98.5%!Bayer FiltersCMOS and CCD detectors are designed to be sensitive to light over the entire visible spectrum. How, then, doe the CMOS detectors on our camera phones measure color? The answer is through the use of Bayer filters. These filters are grids of RGB filters (see Figure 1XX) that are laid over the pixels of the sensor to create color images, through an interpolation of the pixels. You’ll notice that the Bayer filter has two green pixels for every red and blue pixel. This is because the eye is most sensitive to green light, were the Sun’s emission peaks in the visible spectrum.15621005715Figure 1: Bayer Filter Pattern 0Figure 1: Bayer Filter Pattern Read Noise and BiasIntroductionThe first characteristic we will discuss is the read noise of the detector. As the name suggest, this is a source of error in our measurements associated with how the electronics read out the signal from the photon wells. Even in the absence of a signal, and with a sufficiently cooled detected where dark current is negligible (see below) there will still be a noise associated with the electronics of the detector. This is the fundamental limit in the noise of the detector and companies go to great lengths to minimize this noise, with some detectors having read noise much less than one electron – therefore allowing a very accurate measurement of just how many electrons are in your well. The bias level is the initial signal on the chip and is designed to keep the number of counts slightly above zero – even for a zero second exposure. In this section we will look at how to correct for the bias signal in our measurements and how to measure the read noise of the detector – an important source of noise.Collecting the DataMake sure the lens cap is on the detectorTo ensure that the temperature will remain constant – set the temperature to a value near the ambient temperature using the “CIS Calibration” button on the top ribbon. (It looks like a standard settings gear icon)Take two “zero” second exposure by setting the exposure time field on the “CIS Snapshot Control” tab to 0 ms. Save the file using the naming convention explained above.Now take another 100 “zero” second exposures.Also take one exposure at a few longer exposure times (say 1s, 5s, 10s, and 25s).Analyzing the DataThe read noise is measured through the root mean square (or a measure of the noise) in a zero second exposure. If the chip can be assumed uniform it can be determined simply by finding the RMS value in a uniform region on the chip. However, because we cannot truly measure a zero second exposure, we can approximate one by subtracting two separate very short (or “zero” second) exposures, and find the RMS value of a region of this subtracted frame. This is called the “Two Bias” method.Measure the bias by finding the average of a characteristic region of the chip in one of your bias frames. Measure the read noise by looking at the RMS value of the difference of two bias frames in the same region. Divide this RMS value by 2 to get the value of the read noise. Why do we divide by 2? What is the problem with this method (spatial sampling) of determining the bias and read noise? Report your values for the bias and read noise.We determined the bias here through spatial sampling achieving many realizations of the noise by averaging over an area of the chip. Instead of using many pixels of a uniform region to get many measurements of the bias and read noise (spatial sampling), we can instead use many different exposures to get many samples of each pixel to generate a master bias map and determine the read noise for each pixel (temporal sampling). What are the advantages/disadvantages of this method? Which method, spatial or temporal sampling, is more appropriate for a CCD detector? Why? We will now look at the temporal method of determining the bias and read noise.Load the 100 bias matrices into Matlab and find the average and standard deviation for each pixel. This is now a bias and read noise map. Save these maps. Do you notice any difference about the bias and read noise in these temporally averaged images? Is spatial sampling justified?Now that we have measured the bias, we can subtract it from future measurements to remove it from the signal, understanding that the uncertainty in that subtraction is our read noise. Finally, how should the bias and read noise vary in time? Why?Dark CurrentIntroductionAnother important source of noise that is inherent to any detector is the dark current. Even without a signal present (i.e. without any flux on the detector) there can still be an accumulation of charge that is the result of thermal fluctuations generating charges on the chip. This is called the dark current. Like with the bias, the dark current can be subtracted, however, there is still an uncertainty in the signal, which results in additional noise on the chip.Because the dark current is statistically random, the distribution of the thermal signal is Poisson in nature. You will recall from class that this means the uncertainty in the signal is simply the square root of the signal itself. This uncertainty, however, is an additional source of noise in our measurement. The dark current should, in theory, be constant, and therefore vary linearly in time. How should the noise in the dark current vary in time then? Because of the Poisson nature of the dark current, it is not necessary to take spatial or temporal averages to determine the uncertainty, as with the bias/read noise. Note, however, that multiple exposures allow for an additional Nexp reduction in the noise, so multiple exposures are always advantageous (usually a master dark is created, like the master bias, which is the average of several darks). Dark current is measured in [e-/s] and can be determined from the slope of a line fit through a set of zero flux exposures. The dark current also need not be uniform across the chip, as we will see, so measuring it accurately for each pixel is important to characterizing the CMOS detector. In theory, because the dark current is linear, measuring it at one time should tell us the dark current for any exposure. However, because of drift and instabilities in the electronics it is standard practice to take a dark for each exposure.Cooling the detector can help to mitigate the noise of the dark current by reducing the amount of thermal fluctuations that generate charge on the chip. The CMOS detector we are using is equipped with a simple thermal electric cooler (TEC) that allows for the detector to be cooled to -50C below the ambient temperature. Ideally, we would decrease the temperature as much as possible – some CCDs are equipped with TECs that allow for temperatures as low as -50C, which result in dark currents of < 1e-/sec. How do you think the dark current will vary as a function of temperature?In this section we will measure the dark current as a function of time and temperature and determine the noise that it is introduced into our measurements.Collecting the DataMake sure that the lens cap is on the detectorTo ensure that the temperature will remain constant – set the temperature to a value near the ambient temperature using the “CIS Calibration” button on the top ribbon. (It looks like a standard settings gear icon)Measure a bias frame.Measure the dark current at several integration times, roughly doubling the exposure time, until either you approach saturation or reach ~500s integrations (which would be an extremely long integration time if any flux – even a very small one – were incident on the detector). Obtain a minimum of 10 exposures.Now keeping a constant integration time of 5s – vary the temperature of the detector in 1.5C steps to 12C below ambient temperature. (This is the limit of the capabilities of the TEC)Analyzing the DataLoad the varying exposure times for the set temperature into an array in Matlab. Subtract the bias from each frame in the array.Create an error array for your measurements using the SQRT function.Make an errorbar plot for a few pixels of the time varying dark current. Describe the similarities, differences, and features of the curves you see.Write a for loop to go through your array, and using the LSCOV function in Matlab, determine the linear fit for each pixel and obtain the slope and offset, as well as the associated errors. How could we have reduced the error in these measurements? Make an image of the slope and offset of the dark current curve for the chip. Describe what you notice about the dark current across the array. Are there any peculiarities, interesting features, or questionable values? What is the average dark current you measure? What do you notice about the offset? Why is this?We will now look at the dark current as a function of temperature, to see if your guess was correct. We won’t worry about the error in the measurements here, since we are only curious in the functional form.Load your 8 varying temperature measurements into an array in Matlab. Subtract the bias for each frame in the array.Again make a plot for a few pixels of our temperature varying dark current. Do you notice a trend? Describe the similarities, differences, and features of the curves you see.[Optional] If you do not notice a trend, try loading the CCD data supplied. This data covers a much larger temperature range. Plot a few pixels of the temperature vs dark current. Now do you see a trend? Describe the similarities, differences, and features of the curves you see.From this curve, you can see why we try to cool the detector to as low of temperatures as possible and why for extremely low temperatures the dark current can be extremely small, which is necessary to not be dominated by the dark current noise when taking longer exposures of faint objects.GainIntroductionDid you notice a problem with the value you just reported for the dark current? The value you measured was the slope of a line that was counts on the y-axis and time on the x-axis – so it had units of [DN/s]. It was stated, however, that dark current is measured in [e-/s]. What we were missing before was the gain of the detector – that is how many electrons it takes to register a count on the read out electronics. The gain, therefore, has units of [e-/DN]. How is the gain chosen? There are two numbers to consider when setting the gain of a detector. The first is the saturation of the potential well. Because the potential well has a set physical size, there is a limit to the number of electrons it is able to hold. Larger pixel allow for large potential wells. We will discuss later what happens when we overfill these potential wells. The second number comes from the conversion of the analog number of electrons to the digital voltage that is read. This is done by the analog-to-digital converter. The resolution of the converter is defined by a bit number. That is a 16 bit ADC can convert a signal to 216=65536 distinct possible values. The gain is chosen such that the largest number of electrons that a potential well can hold corresponds to the largest possible ADC value. What would the gain be for a detector with a full well of 42840 electrons, read out with a 15 bit ADC?In this section we will determine the gain for our CMOS detector. We can do this through both a spatial and temporal methods, as we did with the bias and read noise. The explanation provided in the analysis below is only an overview. For a more detailed discussion please see the Mirametric technical note found at: the DataCool the detector to as low a temperature as possible. This is to minimize the effects of the dark current.To determine the gain we need exposures at ~10 different flux levels, but want to keep exposure times as short as possible to mitigate the dark current. Choose a flux level such that the longest integration time is 10 second and reaches, on average, 50% full well.Measure a bias frame as well as two different exposures at this flux level.Repeat step 3 for nine additional flux levels, roughly doubling the flux each time. This means your final integration time should be about 10 ms to reach ~50% full well.Analyze the DataBefore analyzing the data, we will briefly discuss how to determine the gain from the frames we just acquired, noting some caveats along the way. Again, for a fuller description, please see the Mirametrics technical note given above.To understand how to measure the gain of the CMOS, we must first note an important property of the nature of light. The arrival of photons at the detector, like the dark current, follows a Poisson distribution. That is, the arrival rates of photons under a constant illumination is not uniform and will have an error that is the square root of the number of photons being received. This directly translates to a noise in the signal that is simply the square root of the signal. The signal we measure is counts, which relates to the number of electrons through the gain. In the form of an equation we have:Se=gSc Ne=gNcwhere “S” is the signal and “N” is the noise, and the subscript “c” corresponds to counts, and “e” corresponds to electrons. As stated, the noise is simply the square root of the signal. Therefore:Nc=1gScThus, if we look at the slope of a signal-variance plot (variance being the square of the noise) for several flux levels we find:Scσc=ScNc2=1gSe(1g)2Se=gThus, the signal-variance plot is simply a straight line and the slope of our plot is simply the gain of our detector! We would be done, therefore, if our chip was perfectly uniform and we had no additional noise terms. Unfortunately, this is not the case. We have other sources of noise such as read noise, dark current, and flat pattern noise that we must account for. These sources of noise actually lead to a non-linearity in our signal-variance plot and, therefore, an underestimation of the gain (see the technical note). Let us briefly, though, look at these noise contributions and see how we can correct them.Bias and Read NoiseFor each flux level we must subtract the bias. This is because the bias contributes to the signal and not the noise. (Remember although we calculate read noise from bias frames it is not the noise in the bias, but rather the noise in the electronics.) Without subtracting the bias, we would therefore preferentially add signal at low flux levels, leading to an underestimation in gain. Why is this an underestimation?The read noise could in theory be measured as the offset of our signal-variance plot (i.e. the noise at zero signal). However, errors in the estimation of the slope are large, and therefore the method used previously is preferred. Fortunately, the read noise is a constant offset and does not affect the slope of the line.Dark CurrentAs you found in the previous section, the noise introduced by the dark current depends on the integration time and temperature of the detector. We attempt to keep exposure times to a minimum and the detector as cool as possible to make the dark current as low as possible. If integration times are longer, or our detector warmer, we have to subtract the dark current from our signal before continuing with our analysis. We will always subtract the dark current from our measurements. Write an equation for our three source of noise so far (assuming we subtract the bias). Is our signal-variance curve still linear?Fixedlat Pattern NoiseFixedlat pattern noise results from the fact that neighboring pixels will vary in sensitivity with respect to one another. This is known as the responsivity of the chip and will be something we will look at later. How does this variation in sensitivity affect our noise? The fact that one pixel may measure 100 counts and a neighboring pixel may measure 110 counts for the same incident flux adds noise that is not captured in the simple photon noise consideration. This additional variance amongst the pixels leads to greater noise for a given signal, and therefore leads to an underestimation of the gain (see technical note). To correct for this flat field variation, we can subtract two frames at the same exposure level to cancel out the flat field contributions and allow for a true estimate of the gain. This is similar logic to how we calculated the read noise, however, there will be a greater variance now due to all our noise sources. Remember, a difference image does not remove the noise – it only zeros the mean value of the image. We are now ready to analyze our data and to get an estimate of the gain of our chip. We can do this through both spatial and temporal methods. Remember, the spatial method relies on getting an accurate measure of the noise by averaging many pixels. The temporal method relies on getting an accurate measure of the noise for each pixel by averaging many frames. Method 1:Load 2 frames of a given flux level into Matlab and subtract the bias and provided dark current from each of them. Now that we finally have some flux on our detector – do you notice any immediate peculiarities in the detector? What might these be?Choose a uniform region (at least 100x100 pixels) on the chip and calculate the average signal in that region for both frames. Is your choice justified? Why or why not?Using your average signals from Step 2, normalize your two frames. Do this by finding the normalization ratio, rnorm=S1S2 , and multiply Frame 2 by rnorm.Subtract your normalized frames to correct for the flat pattern variations. Calculate the variance of this new image in the same region as that used in Step 2. Remember to divide by 2Using your results from Step 2 and Step 5 place a point on your signal-variance plot. Repeat for the remaining flux levels. Once finished, save your signal-variance plot.Using the LSCOV function determine the gain in the region of your chip that you chose. Report this value. What is the error in your gain? Is this gain justified for the whole chip? Why or why not?Method 1 used spatial averaging to obtain an estimate for the gain and assumes the same gain for the entire array. However, we could also use an average and variance of many exposures to get an estimate of the gain for each pixel. Because looking at the whole chip would take many gigabytes of data, for each flux level, we have taken 100 exposures of a small area (100x100 pixels) of the CMOS detector. (Remember this is one advantage of a CMOS over a CCD.)Method 2:Load the 100 images of a given flux level into Matlab and subtract the bias and dark from each of them.Using a 100x100 pixel section, normalize your frames w.r.t. one another. (Refer to Steps 2 & 3 of Method 1) What does this assume about the region we have provided?Taking the average and standard deviation of your 100 frames.Using your results from Step 2 and Step 5 begin populating a signal and variance arrays for each pixel. Repeat for the remaining flux levels.Write a for loop to use the LSCOV function determine the gain for each pixel, using your signal and variance arrays, in the region supplied. Make a gain and error map for your region. Is your error greater or less using this new method? What do you think now of using a single gain for the entire chip?N.B. Step 4 still required a spatial average across the array to correct for any variations in the source intensity over the course of the 100 measurements, and is not using spatial sampling to find the signal/variance as we did in Method 1.Make new read noise and dark current maps that are in the correct units of [e-] and [e-/s]. Make these maps incorporating your two different gain calculations. That is, create a base map using the single gain calculated in Method 1, and update the region where we know the gain specifically for each pixel. Do you notice any difference between the two regions in your maps (i.e. can you measure if the gains differ more than the noise in the gains you measured)?ResponsivityIntroductionAs we mentioned in the previous section – the pixels have a variability in their sensitivity (or responsivity) that results in flat field correction that must be considered. The problem with differencing two separate exposures is that we remove all interesting signal, leaving only the noise. Instead, what would be better, is to have a responsivity array to multiple an image by to normalize out any flat field variations, thus maintaining our signal of interest. But how is this responsivity measured?To answer this, we must first ask what responsivity is. Ultimately, it is a measure of how many electrons are generated for a given number of photons on our detector. Responsivity has units of [e-/ph] and is ultimately a measure of the combined effects of the quantum efficiency (QE) of our detector (i.e. how efficiently are photons turned into countable electrons – ideally this is one-to-one) along with other considerations such as the transmission function of our ND filters and any lenses in the system. The transmission of filters and QE are ultimately a function of wavelength, but because our sensor integrates the signal over the entire optical spectral region, it is difficult to determine their wavelength dependence. For this reason, we will assume a “grey” response for our filters and QE (i.e. independent of wavelength). This is a good approximation for the ND filters, which are grey by design, and an OK approximation for QE and other transmission terms, like from the lens. You can see the QE curve for our detector in the provided documents with this lab. Ultimately, to determine the QE as a function of wavelength would require a wavelength tunable light source to accurately vary the number of photons at a particular wavelength to measure how our counts change in response to such variations in signal.Can we measure the responsivity curve and get an estimate of the QE to compare to the one provided? The answer is yes! Provided there is a calibrated light source, which we just so happen to have. So how do we measure responsivity? Let’s look at a dimensional analysis. As we mentioned, the units of responsivity are:e-ΛWhere e- is the number of electrons and Λ is the number of photons. If we were to expand this we could express this in different units we are more familiar with:e-Λ=Λs-1*e-sThe units of [Λ/s] is a measure of flux. More flux means more photons per unit time. The units of [e-/s] we have already seen. It is the slope of the counts (up to a factor of the gain) vs integration time curve for a given flux. For example, for the dark current we measured, the flux was 0. Therefore if we measure the slope of the counts vs integration times for a variety of fluxes we can measure the responsivity.The question then becomes – how many photons are incident on our detector. We can then divide this by our number of counts/sec in order to obtain the responsivity of our detector. The relationship between counts and photons is given by the camera equation:e-=AΩtgλ1λ2RλSλdλLet’s parse this equations piece by piece to get a better understanding. First there is A, the area of collecting area. For our camera, this area is the area of the lens. For a telescope, it is the area of the primary mirror. It is the amount of collecting area that will be focused onto the detector. Ω is the solid angle of a pixel. That is, although the dish collects light from a large area, each individual pixel is only seeing a small portion of that entire field of view. t is simply our integration time and g the gain. The integral is to integrate the light from the spectral region over which our detector is sensitive. For CCDs and CMOSs that is the entire visible band. For a spectrometer, the spectral region of a given pixel can be very small and depends on the spectrometer’s spectral resolution. R is the responsivity of our detector, while S is the source function (i.e. how does the intensity of light vary as a function of wavelength).Let’s look at these last two terms in a bit more detail. More explicitly R can be defined as:Rλ=TλQE(λ)T(λ) is the transmission of the “system”. This can account for the transmission of the Earth’s atmosphere, for each lens, for each filter, etc. Transmissions of individual elements are always multiplicative. For example, we are using 3 ND filters on our setup. The first blocks ? the incident light, the second blocks ? of the remainder, and the final blocks 1/8 of the remainder of the first two, giving a total reduction in light of 1/64. QE(λ) is the quantum efficiency (explained above) of our detector, what we hope to measure. Because we assume both of these to be grey we can reduce our equation to:R=T*QEand pull both terms out of the integral.So what is S(λ)? S(λ) is simply the source term – it tells us what our incident flux is. This is turn tells us an amount of incident energy, which we can relate to the number of photons incident on our detector. A standard source function used in astronomy is blackbody emission given by Planck’s Law:Bλ,T=2hc2λ51ehcλkT-1 Wm2srμmUsing dimensional analysis, confirm that the units for this source function are correct. This is just an example source function. We will talk more about our source in a moment. What we are interested in, however, is the total number of photons. Remember that the energy of a photon is given by:E=hcλ JΛSo dividing our source function by this we can get:e-=AΩtg*T*QEλ1λ2λhcSλdλSo what is our source function? We will be using a calibrated Labsphere to make our measurements. The Labsphere’s spectral curve has been measured to know exactly how much power is being outputted as a function of wavelength. This curve is provided for you in the data package. The nice thing about this Labsphere is that the wavelength dependence stays the same regardless of flux level, therefore the integral in the above equation is constant, up to a normalization parameter (referenced to the max flux) to account for the variations in the flux level. Therefore, we can solve for QE as:QE= e-AΩtg*T*λ1λ2Sλdλ=e-gtAΩ*T*F*FFo DNsΛs; FFo=68.48where F is simply the measured flux and F is the constant integral of the spectral curve normalized to the maximum flux, Fo. For the transmission, in addition to the ND filter losses, assume an additional 70% loss from the other optics, like lens transmission. Pause for a moment and take the time to make sure you understand the camera equation. What are the units of F,F,& Fo? Unfortunately, our Labsphere was calibrated for the Near-IR, so we will have to make some modification to make it work in the visible, which will we explain below.We are now ready to analyze the data! Our general strategy will be to get a DN/s curve for a variety of fluxes and to plot the slopes of these curves as a function of flux to get a responsivity curve. The slope of this responsivity curve is the QE we are interested in measuring.Collect the DataWe will want to collect data at ~10 different flux levels at ~10 integration times each. Determine 10 reasonable flux levels (i.e. a reasonable saturation time for the highest and lowest fluxes) and the ten integration times at each flux level such that you sample up to ~90% full well in the maximum integration time.Collect a dark frame (make sure the lens cap is on!) for each exposure.Analyze the DataCreate a modified blackbody curve [Optional – this will be provided, but could be fun to try!]Load the provided spectral calibration curve provided in the data package. Note the provided flux values are in mWcm2*sr*μm.We want to fit a modified blackbody curve to our calibration curve. But what temperature should we use? Fit a parabola to the region of peak intensity [.7um, 1um] – the vertex is the peak wavelength. Use Wien’s Law to determine the temperature of the blackbody:Tλmax=2.897*10-3 [m*K]Write a function to make a blackbody curve as a function of wavelength and temperature. And create one that goes from 0 to 2.5 um with the temperature found in Step 2.Evaluate your blackbody function at the same wavelength values as your spectral calibration curve. What is the main difference between these two curves? Evaluate the ratio of the spectral curve to blackbody curve by doing an element-by-element division.Create a modified blackbody curve by multiplying the ratio curve you found in Step 4 with the blackbody curve you created in Step 2. This will scale the blackbody curve to match the functional form and intensity of our calibrated curve. Make a plot of the spectral curve, original blackbody, modified blackbody, and peak fitting parabola. Scale them as needed to fit reasonably.Calculate Responsivity/QELoad your flux frames into an array in Matlab (a 4 dimensional array works well: one axis for flux, one for time, and two for the spatial dimensions).Subtract the dark and bias from each frameUsing your signal, dark current, and read noise, create an error array for your 100 frames. Remember that error adds in quadrature.Using LSCOV fit a line to the set of integration time images for each flux level (your error will come from Step 3). Save these slopes and the error associated with them.Now run the same LSCOV routine using the slopes and their associated errors from Step 4 as your y parameter and the number of photons/sec (determined from the camera equation) as your x parameter. You error in x is simply photon noise (assuming we know all other terms of the camera equation perfectly, which is not the best assumption). The slope LSCOV will give you is a measure of the QE. Make a map of the QE. Is your QE reasonable? How large is the error in QE? What do you think is our largest source of error?Final QuestionTo ensure you did the appropriate background reading, please write a paragraph based off the observations of your calibration report discussing the similarities and differences between a CMOS and CCD described in this write up, explaining two experimental scenarios: one where you would choose a CMOS over a CCD and vice versa. Make sure to discuss the strengths and weaknesses of each detector in yo. ................
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