Tag Archives: read noise

Sub Bit Signal

My camera has a 14-bit ADC.  Can it accurately record information lower than 14 stops below full scale? Can it store sub-LSB signals in the raw data?

With a well designed sensor the answer, unsurprisingly if you’ve followed the last few posts, is yes it can.  The key to being able to capture such tiny visual information in the raw data is a well behaved imaging system with a properly dithered ADCContinue reading Sub Bit Signal

Sub LSB Quantization

This article is a little esoteric so one may want to skip it unless one is interested in the underlying mechanisms that cause quantization error as photographic signal and noise approach the darkest levels of acceptable dynamic range in our digital cameras: one least significant bit in the raw data.  We will use our simplified camera model and deal with Poissonian Signal and Gaussian Read Noise separately – then attempt to bring them together.

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Photographic Sensor Simulation

Physicists and mathematicians over the last few centuries have spent a lot of their time studying light and electrons, the key ingredients of digital photography.  In so doing they have left us with a wealth of theories to explain their behavior in nature and in our equipment.  In this article I will describe how to simulate the information generated by a uniformly illuminated imaging system using open source Octave (or equivalently Matlab) utilizing some of these theories.  Since as you will see the simulations are incredibly (to me) accurate, understanding how the simulator works goes a long way in explaining the inner workings of a digital sensor at its lowest levels; and simulated data can be used to further our understanding of photographic science without having to run down the shutter count of our favorite SLRs.  This approach is usually referred to as Monte Carlo simulation.

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Information Transfer: Non ISO-Invariant Case

We’ve seen how information about a photographic scene is collected in the ISOless/invariant range of a digital camera sensor, amplified, converted to digital data and stored in a raw file.  For a given Exposure the best information quality (IQ) about the scene is available right at the photosites, only possibly degrading from there – but a properly designed** fully ISO invariant imaging system is able to store it in its entirety in the raw data.  It is able to do so because the information carrying capacity (photographers would call it the dynamic range) of each subsequent stage is equal to or larger than the previous one.   Cameras that are considered to be (almost) ISOless from base ISO include the Nikon D7000, D7200 and the Pentax K5.  All digital cameras become ISO invariant above a certain ISO, the exact value determined by design compromises.

Figure 1: Simplified Scene Information Transfer in an ISO Invariant Imaging System at base ISO

In this article we’ll look at a class of imagers that are not able to store the whole information available at the photosites in one go in the raw file for a substantial portion of their working ISOs.  The photographer can in such a case choose out of the full information available at the photosites what smaller subset of it to store in the raw data by the selection of different in-camera ISOs.  Such cameras are sometimes improperly referred to as ISOful. Most Canon DSLRs fall into this category today.  As do kings of darkness such as the Sony a7S or Nikon D5.

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Engineering Dynamic Range in Photography

Dynamic Range (DR) in Photography usually refers to the working tone range, from darkest to brightest, that the imaging system is capable of capturing and/or displaying.  It is expressed as a ratio, in stops:

    \[ DR = log_2(\frac{Maximum Acceptable Signal}{Minimum Acceptable Signal}) \]

It is a key Image Quality metric because photography is all about contrast, and dynamic range limits the range of recordable/displayable tones.  Different components in the imaging system have different working dynamic ranges and the system DR is equal to the dynamic range of the weakest performer in the chain.

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Determining Sensor IQ Metrics: RN, FWC, PRNU, DR, gain – 2

There are several ways to extract Sensor IQ metrics like read noise, Full Well Count, PRNU, Dynamic Range and others from mean and standard deviation statistics obtained from a uniform patch in a camera’s raw file.  In the last post we saw how to do it by using such parameters to make observed data match the measured SNR curve.  In this one we will achieve the same objective by fitting mean and  standard deviation data.  Since the measured data is identical, if the fit is good so should be the results.

Sensor Metrics from Measured Mean and Standard Deviation in DN

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Determining Sensor IQ Metrics: RN, FWC, PRNU, DR, gain – 1

We’ve seen how to model sensors and how to collect signal and noise statistics from the raw data of our digital cameras.  In this post I am going to pull both things together allowing us to estimate sensor IQ metrics: input-referred read noise, clipping/saturation/Full Well Count, Dynamic Range, Pixel Response Non-Uniformities and gain/sensitivity.

There are several ways to extract these metrics from signal and noise data obtained from a camera’s raw file.  I will show two related ones: via SNR in this post and via total noise N in the next.  The procedure is similar and the results are identical.

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Sensor IQ’s Simple Model

Imperfections in an imaging system’s capture process manifest themselves in the form of deviations from the expected signal.  We call these imperfections ‘noise’.   The fewer the imperfections, the lower the noise, the higher the image quality.  However, because the Human Visual System is adaptive within its working range, it’s not the absolute amount of noise that matters to perceived IQ as much as the amount of noise relative to the signal. That’s why to characterize the performance of a sensor in addition to noise we also need to determine its sensitivity and the maximum signal it can detect.

In this series of articles I will describe how to use the Photon Transfer method and a spreadsheet to determine basic IQ performance metrics of a digital camera sensor.  It is pretty easy if we keep in mind the simple model of how light information is converted into raw data by digital cameras:

Sensor photons to DN A


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How to Measure the SNR Performance of Your Digital Camera

Determining the Signal to Noise Ratio (SNR) curves of your digital camera at various ISOs and extracting from them the underlying IQ metrics of its sensor can help answer a number of questions useful to photography.  For instance whether/when to raise ISO;  what its dynamic range is;  how noisy its output could be in various conditions; or how well it is likely to perform compared to other Digital Still Cameras.  As it turns out obtaining the relative data is a little  time consuming but not that hard.  All you need is your camera, a suitable target, a neutral density filter, dcraw and free ImageJ, Octave or (pay) Matlab.

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