Over the last two posts we’ve been exploring some of the differences introduced by tweaks to the Color Filter Array of the Phase One IQ3 100MP Trichromatic Digital Back versus its original incarnation, the Standard Back. Refer to those for the background. In this article we will delve into some of these differences quantitatively.
Let’s start with the compromise color matrices we derived from David Chew’s captures of a ColorChecher 24 in the shade of a sunny November morning in Ohio. These are the matrices necessary to convert white balanced raw data to the perceptual CIE XYZ color space, where it is said there should be one-to-one correspondence with colors as perceived by humans, and therefore where most measurements are performed. They are optimized for each back in the current conditions but they are not perfect, the reason for the word ‘compromise’ in their name:
It is always interesting when innovative companies push the envelope of the state-of-the-art of a single component in their systems because a lot can be learned from before and after comparisons. I was therefore excited when Phase One introduced a Trichromatic version of their Medium Format IQ3 100MP Digital Back last September because it could allows us to isolate the effects of tweaks to their Bayer Color Filter Array, assuming all else stays the same.
Thanks to two virtually identical captures by David Chew at getDPI, and Erik Jaffehr’s intelligent questions at DPR, in the following articles I will explore the effect on linear color of the new Trichromatic CFA (TC) vs the old one on the Standard Back (SB). In the process we will discover that – within the limits of my tests, procedures and understanding – the Standard Back produces apparently more ‘accurate’ color while the Trichromatic produces better looking matrices, potentially resulting in ‘purer’ signals. Continue reading Phase One IQ3 100MP Trichromatic vs Standard Back Linear Color, Part I→
In this article we shall find that the effect of a Bayer CFA on the spatial frequencies and hence the ‘sharpness’ captured by a sensor compared to those from a corresponding monochrome imager can go from nothing to halving the potentially unaliased range based on the chrominance content of the image projected on the sensing plane and the direction in which the spatial frequencies are being stressed.
A Little Sampling Theory
We know from Goodman and previous articles that the sampled image ( ) captured in the raw data by a typical current digital camera can be represented mathematically as the continuous image on the sensing plane ( ) multiplied by a rectangular lattice of Dirac delta functions positioned at the center of each pixel:
with the functions representing the two dimensional grid of delta functions, sampling pitch apart horizontally and vertically. To keep things simple the sensing plane is considered here to be the imager’s silicon itself, which sits below microlenses and other filters so the continuous image is assumed to incorporate their as well as pixel aperture’s effects. Continue reading Bayer CFA Effect on Sharpness→
This post will continue looking at the spatial frequency response measured by MTF Mapper off slanted edges in DPReview.com raw captures and relative fits by the ‘sharpness’ model discussed in the last few articles. The model takes the physical parameters of the digital camera and lens as inputs and produces theoretical directional system MTF curves comparable to measured data. As we will see the model seems to be able to simulate these systems well – at least within this limited set of parameters.
The following fits refer to the green channel of a number of interchangeable lens digital camera systems with different lenses, pixel sizes and formats – from the current Medium Format 100MP champ to the 1/2.3″ 18MP sensor size also sometimes found in the best smartphones. Here is the roster with the cameras as set up:
Having shown that our simple two dimensional MTF model is able to predict the performance of the combination of a perfect lens and square monochrome pixel we now turn to the effect of the sampling interval on spatial resolution according to the guiding formula:
The hats in this case mean the Fourier Transform of the relative component normalized to 1 at the origin (), that is the individual MTFs of the perfect lens PSF, the perfect square pixel and the delta grid.
Sampling in the Spatial and Frequency Domains
Sampling is expressed mathematically as a Dirac delta function at the center of each pixel (the red dots below).
The next few posts will describe a linear spatial resolution model that can help a photographer better understand the main variables involved in evaluating the ‘sharpness’ of photographic equipment and related captures. I will show numerically that the combined spectral frequency response (MTF) of a perfect AAless monochrome digital camera and lens in two dimensions can be described as the normalized multiplication of the Fourier Transform (FT) of the lens Point Spread Function by the FT of the (square) pixel footprint, convolved with the FT of a rectangular grid of Dirac delta functions centered at each pixel, as better described in the article
With a few simplifying assumptions we will see that the effect of the lens and sensor on the spatial resolution of the continuous image on the sensing plane can be broken down into these simple components. The overall ‘sharpness’ of the captured digital image can then be estimated by combining the ‘sharpness’ of each of them. Continue reading A Simple Model for Sharpness in Digital Cameras – I→
While perusing Jim Kasson’s excellent Longitudinal Chromatic Aberration tests I was impressed by the quantity and quality of the information the resulting data provides. Longitudinal, or Axial, CA is a form of defocus and as such it cannot be effectively corrected during raw conversion, so having a lens well compensated for it will provide a real and tangible improvement in the sharpness of final images. How much of an improvement?
This is a vast and complex subject for which I do not have formal training. In this and the previous article I present my thoughts on how MTF50 results obtained from raw data of the four Bayer CFA channels off a uniformly illuminated neutral target captured with a typical digital camera through the slanted edge method can be combined to provide a meaningful composite MTF50 for the imaging system as a whole1. Corrections, suggestions and challenges are welcome. Continue reading COMBINING BAYER CFA MTF Curves – II→
This is a vast and complex subject for which I do not have formal training. In this and the following article I will discuss my thoughts on how MTF50 results obtained from raw data of the four Bayer CFA color channels off a neutral target captured with a typical camera through the slanted edge method can be combined to provide a meaningful composite MTF50 for the imaging system as a whole. The perimeter are neutral slanted edge measurements of Bayer CFA raw data for linear spatial resolution (‘sharpness’) photographic hardware evaluations. Corrections, suggestions and challenges are welcome. Continue reading Combining Bayer CFA Modulation Transfer Functions – I→
For the purposes of ‘sharpness’ spatial resolution measurement in photography cameras can be considered shift-invariant, linear systems.
Shift invariant means that the imaging system should respond exactly the same way no matter where light from the scene falls on the sensing medium . We know that in a strict sense this is not true because for instance a pixel has a square area so it cannot have an isotropic response by definition. However when using the slanted edge method of linear spatial resolution measurement we can effectively make it shift invariant by careful preparation of the testing setup. For example the edges should be slanted no more than this and no less than that. Continue reading Linearity in the Frequency Domain→
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→
Whether the human visual system perceives a displayed slow changing gradient of tones, such as a vast expanse of sky, as smooth or posterized depends mainly on two well known variables: the Weber-Fechner Fraction of the ‘steps’ in the reflected/produced light intensity (the subject of this article); and spatial dithering of the light intensity as a result of noise (the subject of a future one).
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.
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.
In the last few posts I have made the case that Image Quality in a digital camera is entirely dependent on the light Information collected at a sensor’s photosites during Exposure. Any subsequent processing – whether analog amplification and conversion to digital in-camera and/or further processing in-computer – effectively applies a set of Information Transfer Functions to the signal that when multiplied together result in the data from which the final photograph is produced. Each step of the way can at best maintain the original Information Quality (IQ) but in most cases it will degrade it somewhat.
IQ: Only as Good as at Photosites’ Output
This point is key: in a well designed imaging system** the final image IQ is only as good as the scene information collected at the sensor’s photosites, independently of how this information is stored in the working data along the processing chain, on its way to being transformed into a pleasing photograph. As long as scene information is properly encoded by the system early on, before being written to the raw file – and information transfer is maintained in the data throughout the imaging and processing chain – final photograph IQ will be virtually the same independently of how its data’s histogram looks along the way.
In photography, digital cameras capture information about the scene carried by photons reflected by it and store the information as data in a raw file pretty well linearly. Data is the container, scene information is the substance. There may or may not be information in the data, no matter what its form. With a few limitations what counts is the substance, information, not the form, data.
A Simple Example
Imagine for instance that you are taking stock of the number of remaining pieces in your dinner place settings. You originally had a full set of 6 of everything but today, after many years of losses and breakage, this is the situation in each category: Continue reading The Difference Between Data and Information→
We know that the best Information Quality possible collected from the scene by a digital camera is available right at the output of the sensor and it will only be degraded from there. This article will discuss what happens to this information as it is transferred through the imaging system and stored in the raw data. It will use the simple language outlined in the last post to explain how and why the strategy for Capturing the best Information or Image Quality (IQ) possible from the scene in the raw data involves only two simple steps:
1) Maximizing the collected Signal given artistic and technical constraints; and
2) Choosing what part of the Signal to store in the raw data and what part to leave behind.
The second step is only necessary if your camera is incapable of storing the entire Signal at once (that is it is not ISO invariant) and will be discussed in a future article. In this post we will assume an ISOless imaging system.
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.
When photographers talk about grayscale ‘tones’ they typically refer to the number of distinct gray levels present in a displayed image. They don’t want to see distinct levels in a natural slow changing gradient like a dark sky: if it’s smooth they want to perceive it as smooth when looking at their photograph. So they want to make sure that all possible tonal information from the scene has been captured and stored in the raw data by their imaging system.
My camera has an engineering Dynamic Range of 14 stops, how many bits do I need to encode that DR? Well, to encode the whole Dynamic Range 1 bit will suffice. The reason is simple, dynamic range is only concerned with the extremes, not with tones in between:
So in theory we only need 1 bit to encode it: zero for minimum signal and one for maximum signal, like so
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:
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.
Most of the photographs captured these days end up being viewed on a display of some sort, with at best 4K (4096×2160) but often no better than HD resolution (1920×1080). Since the cameras that capture them have typically several times that number of pixels, 6000×4000 being fairly normal today, most images need to be substantially downsized for viewing, even allowing for some cropping. Resizing algorithms built into browsers or generic image viewers tend to favor expediency over quality, so it behooves the IQ conscious photographer to manage the process, choosing the best image size and downsampling algorithm for the intended file and display medium.
When downsizing the objective is to maximize the original spatial resolution retained while minimizing the possibility of aliasing and moirè. In this article we will take a closer look at some common downsizing algorithms and their effect on spatial resolution information in the frequency domain.
In fact the question is more generic than that. Smaller format lens designers try to compensate for their imaging system geometric resolution penalty (compared to a larger format when viewing final images at the same size) by designing ‘sharper’ lenses specifically for it, rather than recycling larger formats’ designs (feeling guilty APS-C?) – sometimes with excellent effect. Are they succeeding? I will use mFT only as an example here, but input is welcome for all formats, from phones to large format.
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
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.
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:
A reader suggested that a High-Res Olympus E-M5 Mark II image used in the previous post looked sharper than the equivalent Sony a6000 image, contradicting the relative MTF50 measurements, perhaps showing ‘the limitations of MTF50 as a methodology’. That would be surprising because MTF50 normally correlates quite well with perceived sharpness, so I decided to check this particular case out.
‘Who are you going to believe, me or your lying eyes’?
Olympus just announced the E-M5 Mark II, an updated version of its popular micro Four Thirds E-M5 model, with an interesting new feature: its 16MegaPixel sensor, presumably similar to the one in other E-Mx bodies, has a high resolution mode where it gets shifted around by the image stabilization servos during exposure to capture, as they say in their press release
‘resolution that goes beyond full-frame DSLR cameras. 8 images are captured with 16-megapixel image information while moving the sensor by 0.5 pixel steps between each shot. The data from the 8 shots are then combined to produce a single, super-high resolution image, equivalent to the one captured with a 40-megapixel image sensor.’
A great idea that could give a welcome boost to the ‘sharpness’ of this handy system. This preliminary test shows that the E-M5 mk II 64MP High-Res mode gives in this case a 10-12% advantage in MTF50 linear spatial resolution compared to the Standard Shot 16MP mode. Plus it apparently virtually eliminates the possibility of aliasing and moiré. Great stuff, Olympus.
So, is it true that a Four Thirds lens needs to be about twice as ‘sharp’ as its Full Frame counterpart in order to be able to display an image of spatial resolution equivalent to the larger format’s?
It is, because of the simple geometry I will describe in this article. In fact with a few provisos one can generalize and say that lenses from any smaller format need to be ‘sharper’ by the ratio of their sensor linear sizes in order to produce the same linear resolution on same-sized final images.
This is one of the reasons why Ansel Adams shot 4×5 and 8×10 – and I would too, were it not for logistical and pecuniary concerns.
Several sites perform spatial resolution ‘sharpness’ testing of imaging systems for photographers (i.e. ‘lens+digital camera’) and publish results online. You can also measure your own equipment relatively easily to determine how sharp your hardware is. However comparing results from site to site and to your own can be difficult and/or misleading, starting from the multiplicity of units used: cycles/pixel, line pairs/mm, line widths/picture height, line pairs/image height, cycles/picture height etc.
This post will address the units involved in spatial resolution measurement using as an example readings from the slanted edge method.
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.
Effective Quantum Efficiency as I calculate it is an estimate of the probability that a visible photon – from a ‘Daylight’ blackbody radiating source at a temperature of 5300K impinging on the sensor in question after making it through its IR filter, UV filter, AA low pass filter, microlenses, average Color Filter – will produce a photoelectron upon hitting silicon:
One of the fairest ways to compare the performance of two cameras of different physical characteristics and specifications is to ask a simple question: which photograph would look better if the cameras were set up side by side, captured identical scene content and their output were then displayed and viewed at the same size?
Achieving this set up and answering the question is anything but intuitive because many of the variables involved, like depth of field and sensor size, are not those we are used to dealing with when taking photographs. In this post I would like to attack this problem by first estimating the output signal of different cameras when set up to capture Equivalent images.
It’s a bit long so I will give you the punch line first: digital cameras of the same generation set up equivalently will typically generate more or less the same signal in independently of format. Ignoring noise, lenses and aspect ratio for a moment and assuming the same camera gain and number of pixels, they will produce identical raw files. Continue reading Equivalence and Equivalent Image Quality: Signal→
You have obtained a raw file containing the image of a slanted edge captured with good technique. How do you get the MTF curve of the camera and lens combination that took it? Download and feast your eyes on open source MTF Mapper by Frans van den Bergh. No installation required, simply store it in its own folder.
My preferred method for measuring the spatial resolution performance of photographic equipment these days is the slanted edge method. It requires a minimum amount of additional effort compared to capturing and simply eye-balling a pinch, Siemens or other chart but it gives immensely more, useful, accurate, absolute information in the language and units that have been used to characterize optical systems for over a century: it produces a good approximation to the Modulation Transfer Function of the two dimensional Point Spread Function of the camera/lens system in the direction perpendicular to the edge.
Much of what there is to know about a system’s spatial resolution performance can be deduced by analyzing such a curve, starting from the perceptually relevant MTF50 metric, discussed a while back. And all of this simply from capturing the image of a black and white slanted edge, which one can easily produce and print at home.
Why Raw? The question is whether one is interested in measuring the objective, quantitative spatial resolution capabilities of the hardware or whether instead one would prefer to measure the arbitrary, qualitatively perceived sharpening prowess of (in-camera or in-computer) processing software as it turns the capture into a pleasing final image. Either is of course fine.
My take on this is that the better the IQ captured the better the final image will be after post processing. In other words I am typically more interested in measuring the spatial resolution information produced by the hardware comfortable in the knowledge that if I’ve got good quality data to start with its appearance will only be improved in post by the judicious use of software. By IQ here I mean objective, reproducible, measurable physical quantities representing the quality of the information captured by the hardware, ideally in scientific units.
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? Continue reading How Sharp are my Camera and Lens?→
The in-camera ISO dial is a ballpark milkshake of an indicator to help choose parameters that will result in a ‘good’ perceived picture. Key ingredients to obtain a ‘good’ perceived picture are 1) ‘good’ Exposure and 2) ‘good’ in-camera or in-computer processing. It’s easier to think about them as independent processes and that comes naturally to you because you shoot raw in manual mode and you like to PP, right? Continue reading Exposure and ISO→