Tag Archives: quanta

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 such a spectrum 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.

Continue reading The Spectral Response of Digital Cameras →

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.

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Information Science, IQ, Quantization, Sensors

Sub Bit Signal

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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 ADC.  Continue reading Sub Bit Signal →