Tag Archives: photon

Color, Exposure, Photometry, Radiometry, Sensors

Connecting Photographic Raw Data to Tristimulus Color Science

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Absolute Raw Data

In the previous article we determined that the three r_{_L}g_{_L}b_{_L} values recorded in the raw data in the center of the image plane in units of Data Numbers per pixel – by a digital camera and lens as a function of absolute spectral radiance L(\lambda) at the lens – can be estimated as follows:

(1)   \begin{equation*} r_{_L}g_{_L}b_{_L} =\frac{\pi p^2 t}{4N^2} \int\limits_{380}^{780}L(\lambda) \odot SSF_{rgb}(\lambda) d\lambda \end{equation*}

with subscript _L indicating absolute-referred units and SSF_{rgb} the three system Spectral Sensitivity Functions.   In this series of articles \odot is wavelength by wavelength multiplication (what happens to the spectrum of light as it progresses through the imaging system) and the integral just means the area under each of the three resulting curves (integration is what the pixels do during exposure).  Together they represent an inner or dot product.  All variables in front of the integral were previously described and can be considered constant for a given photographic setup. Continue reading Connecting Photographic Raw Data to Tristimulus Color Science →

Color, Exposure, Photometry, Radiometry, Sensors

The Physical Units of Raw Data

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In the previous article we (I) learned that the Spectral Sensitivity Functions of a given digital camera and lens are the result of the interaction of light from the scene with all of the spectrally varied components that make up the imaging system: mainly the lens, ultraviolet/infrared hot mirror, Color Filter Array and other filters, finally the photoelectric layer of the sensor, which is normally silicon in consumer kit.

Figure 1. The journey of light from source to sensor.  Cone Ω will play a starring role in the narrative that follows.

In this one we will put the process on a more formal theoretical footing, setting the stage for the next few on the role of white balance.

Continue reading The Physical Units of Raw Data →

Color, Exposure, Photometry, Radiometry, Sensors

The Spectral Response of Digital Cameras

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Photography works because visible light from one or more sources reaches the scene and is reflected in the direction of the camera, which then captures a signal proportional to it.  The journey of light can be described in integrated units of power all the way to the sensor, for instance so many watts per square meter. However ever since Newton we have known that such total power is in fact the result of the weighted sum of contributions by every frequency  that makes up the light, what he called its spectrum.

Our ability to see and record color depends on knowing the distribution of the power contained within a subset of these frequencies and how it interacts with the various objects in its path.  This article is about how a typical digital camera for photographers interacts with the spectrum arriving from the scene: we will dissect what is sometimes referred to as the system’s Spectral Response or Sensitivity.

Figure 1. Spectral Sensitivity Functions of an arbitrary imaging system, resulting from combining the responses of the various components described in the article.

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IQ, Raspberry Pi, Sensors

Pi HQ Cam Sensor Performance

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Now that we know how to open 12-bit raw files captured with the new Raspberry Pi High Quality Camera, we can learn a bit more about the capabilities of its 1/2.3″ Sony IMX477 sensor from a keen photographer’s perspective.  The subject is a bit dry, so I will give you the summary upfront.  These figures were obtained with my HQ module at room temperature and the raspistill – -raw (-r) command:

Raspberry Pi
HQ Camera		raspistill
--raw -ag 1		Comments
Black Level256.3 DN256.0 - 257.3 based on gain
White Level4095Constant throughout
Analog Gain1Gain Range 1 - 16
Read Noise3 e-, gain 1
1.5 e-, gain 16		1.53 DN from black frame
11.50 DN
Clipping (FWC)8180 e-at base gain, 3400e-/um^2
Dynamic Range11.15 stops
11.3 stops		SNR = 1 to Clipping
Read Noise to Clipping
System Gain0.47 DN/e-at base analog gain
Star Eater AlgorithmPartly DefeatableAll channels - from base gain and from min shutter speed
Low Pass FilterYesAll channels - from base gain and from min shutter speed

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ACR, Banding, Color, Exposure, Perceptual, Photometry, Processing

Linear Color: Applying the Forward Matrix

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Now that we know how to create a 3×3 linear matrix to convert white balanced and demosaiced raw data into XYZ_{D50}  connection space – and where to obtain the 3×3 linear matrix to then convert it to a standard output color space like sRGB – we can take a closer look at the matrices and apply them to a real world capture chosen for its wide range of chromaticities.

Figure 1. Image with color converted using the forward linear matrix discussed in the article.

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ACR, Color, LR, Perceptual, Processing

Color: Determining a Forward Matrix for Your Camera

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We understand from the previous article that rendering color with Adobe DNG raw conversion essentially means mapping raw data in the form of rgb triplets into a standard color space via a Profile Connection Space in a two step process

    \[ Raw Data \rightarrow XYZ_{D50} \rightarrow RGB_{standard} \]

The first step white balances and demosaics the raw data, which at that stage we will refer to as rgb, followed by converting it to XYZ_{D50} Profile Connection Space through linear projection by an unknown ‘Forward Matrix’ (as DNG calls it) of the form

(1)   \begin{equation*} \left[ \begin{array}{c} X_{D50} \\ Y_{D50} \\ Z_{D50} \end{array} \right] = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix} \left[ \begin{array}{c} r \\ g \\ b \end{array} \right] \end{equation*}

with data as column-vectors in a 3xN array.  Determining the nine a coefficients of this matrix M is the main subject of this article[1]. Continue reading Color: Determining a Forward Matrix for Your Camera →

Color, Perceptual, Photometry, Processing, Radiometry

Color: From Object to Eye

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How do we translate captured image information into a stimulus that will produce the appropriate perception of color?  It’s actually not that complicated[1].

Recall from the introductory article that a photon absorbed by a cone type (\rho, \gamma or \beta) in the fovea produces the same stimulus to the brain regardless of its wavelength[2].  Take the example of the eye of an observer which focuses  on the retina the image of a uniform object with a spectral photon distribution of 1000 photons/nm in the 400 to 720nm wavelength range and no photons outside of it.

Because the system is linear, cones in the foveola will weigh the incoming photons by their relative sensitivity (probability) functions and add the result up to produce a stimulus proportional to the area under the curves.  For instance a \gamma cone may see about 321,000 photons arrive and produce a relative stimulus of about 94,700, the weighted area under the curve:

equal-photons-per-wl
Figure 1. Light made up of 321k photons of broad spectrum and constant Spectral Photon Distribution between 400 and 720nm  is weighted by cone sensitivity to produce a relative stimulus equivalent to 94,700 photons, proportional to the area under the curve

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Color, Exposure, Perceptual, Photometry, Radiometry

An Introduction to Color in Digital Cameras

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This article will set the stage for a discussion on how pleasing color is produced during raw conversion.  The easiest way to understand how a camera captures and processes ‘color’ is to start with an example of how the human visual system does it.

An Example: Green

Light from the sun strikes leaves on a tree.   The foliage of the tree absorbs some of the light and reflects the rest diffusely  towards the eye of a human observer.  The eye focuses the image of the foliage onto the retina at its back.  Near the center of the retina there is a small circular area called fovea centralis which is dense with light receptors of well defined spectral sensitivities called cones. Information from the cones is pre-processed by neurons and carried by nerve fibers via the optic nerve to the brain where, after some additional psychovisual processing, we recognize the color of the foliage as green[1].

spd-to-cone-quanta3
Figure 1. The human eye absorbs light from an illuminant reflected diffusely by the object it is looking at.

Continue reading An Introduction to Color in Digital Cameras →

IQ, Sensors

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

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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

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

IQ, Sensors

Sensor IQ’s Simple Model

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Imperfections in an imaging system’s capture process manifest themselves in the form of deviations from the expected signal.  We call these imperfections ‘noise’ because they introduce grain and artifacts in our images.   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 Image Quality (IQ) as much as the amount of noise relative to the signal – represented for instance by the Signal to Noise Ratio (SNR). That’s why to characterize the performance of a sensor in addition to signal and 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
Figure 1.

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Exposure, Photometry, Radiometry, Sensors

How Many Photons on a Pixel at a Given Exposure

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How many photons impinge on a pixel illuminated by a known light source during exposure?  To answer this question in a photographic context under daylight we need to know the effective area of the pixel, the Spectral Power Distribution of the illuminant and the relative Exposure.

We can typically estimate the pixel’s effective area and the Spectral Power Distribution of the illuminant – so all we need to determine is what Exposure the relative irradiance corresponds to in order to obtain the answer.

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Exposure, Radiometry

Photons Emitted by Light Source

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How many photons are emitted by a light source? To answer this question we need to evaluate the following simple formula at every wavelength in the spectral range of interest and add the values up:

(1)   \begin{equation*} \frac{\text{Power of Light in }W/m^2}{\text{Energy of Average Photon in }J/photon} \end{equation*}

The Power of Light emitted in W/m^2 is called Spectral Exitance, with the symbol M_e(\lambda) when referred to  units of energy.  The energy of one photon at a given wavelength is

(2)   \begin{equation*} e_{ph}(\lambda) = \frac{hc}{\lambda}\text{ joules/photon} \end{equation*}

with \lambda the wavelength of light in meters and h and c Planck’s constant and the speed of light in the chosen medium respectively.  Since Watts are joules per second the units of (1) are therefore photons/m^2/s.  Writing it more formally:

(3)   \begin{equation*} M_{ph} = \int\limits_{\lambda_1}^{\lambda_2} \frac{M_e(\lambda)\cdot \lambda \cdot d\lambda}{hc} \text{ $\frac{photons}{m^2\cdot s}$} \end{equation*}

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