Tag Archives: digital

illuminant, Information Science, Quantization, Sensors, SPD, variation

Photons, Shot Noise and Poisson Processes

May 17, 2023 Jack Leave a comment

Every digital photographer soon discovers that there are three main sources of visible random noise that affect pictures taken in normal conditions: Shot, pixel response non-uniformities (PRNU) and Read noise.^[1]

Shot noise (sometimes referred to as Photon Shot Noise or Photon Noise) we learn is ‘inherent in light’; PRNU is per pixel gain variation proportional to light, mainly affecting the brighter portions of our pictures; Read Noise is instead independent of light, introduced by the electronics and visible in the darker shadows. You can read in this earlier post a little more detail on how they interact.

However, shot noise is omnipresent and arguably the dominant source of visible noise in typical captures. This article’s objective is to dig deeper into the sources of Shot Noise that we see in our photographs: is it really ‘inherent in the incoming light’? What about if the incoming light went through clouds or was reflected by some object at the scene? And what happens to the character of the noise as light goes through the lens and is turned into photoelectrons by a pixel’s photodiode?

Fish, dear reader, fish and more fish.

Continue reading Photons, Shot Noise and Poisson Processes →

Banding, IQ, Sensors

The HV Spectrogram

November 16, 2019 Jack 3 Comments

A spectrogram, also sometimes referred to as a periodogram, is a visual representation of the Power Spectrum of a signal. Power Spectrum answers the question “How much power is contained in the frequency components of the signal”. In digital photography a Power Spectrum can show the relative strength of repeating patterns in captures and whether processing has been applied.

In this article I will describe how you can construct a spectrogram and how to interpret it, using dark field raw images taken with the lens cap on as an example. This can tell us much about the performance of our imaging devices in the darkest shadows and how well tuned their sensors are there.

Pixel level noise spectrum — Figure 1. Horizontal and Vertical Spectrogram of noise captured in the raw data by a Nikon Z7 at base ISO with the lens cap on. The plot shows clear evidence of low-pass filtering in the blue CFA color plane and pattern noise repeating every 6 rows there and in one of the green ones.

Continue reading The HV Spectrogram →

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

Linear Color: Applying the Forward Matrix

December 12, 2016 Jack Leave a comment

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.

Continue reading Linear Color: Applying the Forward Matrix →

ACR, Color, LR, Perceptual, Processing

Color: Determining a Forward Matrix for Your Camera

December 7, 2016 Jack 31 Comments

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

December 4, 2016 Jack Leave a comment

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

Continue reading Color: From Object to Eye →

Color, Exposure, Perceptual, Photometry, Radiometry

An Introduction to Color in Digital Cameras

November 27, 2016 Jack 2 Comments

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 →

Information Science, IQ, Sensors

Information Theory for Photographers

May 21, 2015 Jack Leave a comment

Ever since Einstein we’ve been able to say that humans ‘see’ because information about the scene is carried to the eyes by photons reflected by it. So when we talk about Information in photography we are referring to information about the energy and distribution of photons arriving from the scene. The more complete this information, the better we ‘see’. No photons = no information = no see; few photons = little information = see poorly = poor IQ; more photons = more information = see better = better IQ.

Sensors in digital cameras work similarly, their output ideally being the energy and location of every photon incident on them during Exposure. That’s the full information ideally required to recreate an exact image of the original scene for the human visual system, no more and no less. In practice however we lose some of this information along the way during sensing, so we need to settle for approximate location and energy – in the form of photoelectron counts by pixels of finite area, often correlated to a color filter array.

Continue reading Information Theory for Photographers →

Equivalence, Formats, Sensors

Equivalence in Pictures: Focal Length, f-number, diffraction, DOF

January 31, 2015 Jack Leave a comment

Equivalence – as we’ve discussed one of the fairest ways to compare the performance of two cameras of different physical formats, characteristics and specifications – essentially boils down to two simple realizations for digital photographers:

metrics need to be expressed in units of picture height (or diagonal where the aspect ratio is significantly different) in order to easily compare performance with images displayed at the same size; and
focal length changes proportionally to sensor size in order to capture identical scene content on a given sensor, all other things being equal.

The first realization should be intuitive (see next post). The second one is the subject of this post: I will deal with it through a couple of geometrical diagrams.

Continue reading Equivalence in Pictures: Focal Length, f-number, diffraction, DOF →

IQ, Perceptual, Sharpening, Spatial Resolution

How Sharp are my Camera and Lens?

October 1, 2014 Jack Leave a comment

You want to measure how sharp your camera/lens combination is to make sure it lives up to its specs. Or perhaps you’d like to compare how well one lens captures spatial resolution compared to another you own. Or perhaps again you are in the market for new equipment and would like to know what could be expected from the shortlist. Or an old faithful is not looking right and you’d like to check it out. So you decide to do some testing. Where to start?

In the next four articles I will walk you through my methodology based on captures of slanted edge targets:

Continue reading How Sharp are my Camera and Lens? →

Exposure

What Is Exposure

August 27, 2014 Jack 2 Comments

When capturing a typical photograph, light from one or more sources is reflected from the scene, reaches the lens, goes through it and eventually hits the sensing plane.

In photography Exposure is the quantity of visible light per unit area incident on the image plane during the time that it is exposed to the scene. Exposure is intuitively proportional to Luminance from the scene $L$ and exposure time $t$. It is inversely proportional to lens f-number $N$ squared because it determines the relative size of the cone of light captured from the scene. You can read more about the theory in the article on angles and the Camera Equation.

Continue reading What Is Exposure →

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