Tag Archives: modulation transfer function

IQ, Optics, Sharpness, Spatial Resolution

What is Resolution?

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In photography Resolution refers to the ability of an imaging system to capture fine detail from the scene, making it a key determinant of Image Quality.  For instance, with high resolution equipment we might be able to count the number of tiny leaves on a distant tree, while we might not with a lower-res one.  Or the leaves might look sharp with the former and unacceptably mushy with the latter.

We quantify resolution by measuring detail contrast after it has been inevitably smeared by the imaging process.  As detail becomes smaller and closer together in the image, the blurred darker and lighter parts start mixing together until the relative contrast decreases to the point that it disappears, a limit referred to as  diffraction extinction, beyond which all detail is lost and no additional spatial information can be captured from the scene.

Sinusoidal target of increasing frequency to diffraction limit extinction
Increasingly small detail smeared by the imaging process, highly magnified.

The units of resolution are spatial frequencies, the inverse of the size and distance of the detail in question.  Of course at diffraction extinction no visual information is captured, therefore in most cases the criteria for usability are set by larger detail than that – or equivalently at lower frequencies.  Thresholds tend to be application specific and arbitrary.

The type of resolution being measured must also be specified since the term can be applied to different physical quantities: sensor, spatial, temporal, spectral, type of light, medium etc.  In photography we are normally interested in Spatial Resolution from incoherent light traveling in air so that will be the focus here.

Continue reading What is Resolution? →

Fourier Optics, MTF, PSF, Sharpness, Spatial Resolution

Introduction to Texture MTF

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Texture MTF is a method to measure the sharpness of a digital camera and lens by capturing the image of a target of known characteristics.  It purports to better evaluate the perception of fine details in low contrast areas of the image – what is referred to as ‘texture’ – in the presence of noise reduction, sharpening or other non-linear processing performed by the camera before writing data to file.

Figure 1. Image of Dead Leaves low contrast target. Such targets are designed to have controlled scale and direction invariant features with a power law Power Spectrum.

The Modulation Transfer Function (MTF) of an imaging system represents its spatial frequency response,  from which many metrics related to perceived sharpness are derived: MTF50, SQF, SQRI, CMT Acutance etc.  In these pages we have used to good effect the slanted edge method to obtain accurate estimates of a system’s MTF curves in the past.[1]

In this article we will explore proposed methods to determine Texture MTF and/or estimate the Optical Transfer Function of the imaging system under test from a reference power-law Power Spectrum target.  All three rely on variations of the ratio of captured to reference image in the frequency domain: straight Fourier Transforms; Power Spectral Density; and Cross Power Density.  In so doing we will develop some intuitions about their strengths and weaknesses. Continue reading Introduction to Texture MTF →

Fourier Optics, Geometrical Optics, MTF, PSF, wavefront

Fourier Optics and the Complex Pupil Function

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In the last article we learned that a complex lens can be modeled as just an entrance pupil, an exit pupil and a geometrical optics black-box in between.  Goodman[1] suggests that all optical path errors for a given Gaussian point on the image plane can be thought of as being introduced by a custom phase plate at the pupil plane, delaying or advancing the light wavefront locally according to aberration function \Delta W(u,v) as earlier described.

The phase plate distorts the forming wavefront, introducing diffraction and aberrations, while otherwise allowing us to treat the rest of the lens as if it followed geometrical optics rules.  It can be associated with either the entrance or the exit pupil.  Photographers are usually concerned with the effects of the lens on the image plane so we will associate it with the adjacent Exit Pupil.

aberrations coded as phase plate in exit pupil generalized complex pupil function
Figure 1.  Aberrations can be fully described by distortions introduced by a fictitious phase plate inserted at the uv exit pupil plane.  The phase error distribution is the same as the path length error described by wavefront aberration function ΔW(u,v), introduced in the previous article.

Continue reading Fourier Optics and the Complex Pupil Function →

Fourier Optics, Geometrical Optics, intensity, MTF, Optics, PSF, wavefront

An Introduction to Pupil Aberrations

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As discussed in the previous article, so far we have assumed ideal optics, with spherical wavefronts propagating into and out of the lens’ Entrance and Exit pupils respectively.  That would only be true if there were no aberrations. In that case the photon distribution within the pupils would be uniform and such an optical system would be said to be diffraction limited.

Figure 1.   Optics as a black box, fully described for our purposes by its terminal properties at the Entrance and Exit pupils.  A horrible attempt at perspective by your correspondent: the Object, Pupils and Image planes should all be parallel and share the optical axis z.

On the other hand if lens imperfections, aka aberrations, were present the photon distribution in the Exit Pupil would be distorted, thus unable to form a perfectly  spherical wavefront out of it, with consequences for the intensity distribution of photons reaching the image.

Either pupil can be used to fully describe the light collection and concentration characteristics of a lens.  In imaging we are typically interested in what happens after the lens so we will choose to associate the performance of the optics with the Exit Pupil. Continue reading An Introduction to Pupil Aberrations →

DOF, Optics, Sensors, Sharpening, Sharpness, Spatial Resolution

Diffracted DOF Aperture Guides: 24-35mm

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As a landscape shooter I often wonder whether old rules for DOF still apply to current small pixels and sharp lenses. I therefore roughly measured  the spatial resolution performance of my Z7 with 24-70mm/4 S in the center to see whether ‘f/8 and be there’ still made sense today.  The journey and the diffraction-simple-aberration aware model were described in the last few posts.  The results are summarized in the Landscape Aperture-Distance charts presented here for the 24, 28 and 35mm focal lengths.

I also present the data in the form of a simplified plot to aid making the right compromises when the focusing distance is flexible.  This information is valid for the Z7 and kit in the center only.  It probably just as easily applies to cameras with similarly spec’d pixels and lenses. Continue reading Diffracted DOF Aperture Guides: 24-35mm →

DOF, IQ, Perceptual, Sharpness, Spatial Resolution

DOF and Diffraction: 24mm Guidelines

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After an exhausting two and a half hour hike you are finally resting, sitting on a rock at the foot of your destination, a tiny alpine lake, breathing in the thin air and absorbing the majestic scenery.  A cool light breeze suddenly rips the surface of the water, morphing what has until now been a perfect reflection into an impressionistic interpretation of the impervious mountains in the distance.

The beautiful flowers in the foreground are so close you can touch them, the reflection in the water 10-20m away, the imposing mountains in the background a few hundred meters further out.  You realize you are hungry.  As you search the backpack for the two panini you prepared this morning you begin to ponder how best to capture the scene: subject,  composition, Exposure, Depth of Field.

Figure 1. A typical landscape situation: a foreground a few meters away, a mid-ground a few tens and a background a few hundred meters further out.  Three orders of magnitude.  The focus point was on the running dog, f/16, 1/100s.  Was this a good choice?

Depth of Field.  Where to focus and at what f/stop?  You tip your hat and just as you look up at the bluest of blue skies the number 16 starts enveloping your mind, like rays from the warm noon sun. You dial it in and as you squeeze the trigger that familiar nagging question bubbles up, as it always does in such conditions.  If this were a one shot deal, was that really the best choice?

In this article we attempt to provide information to make explicit some of the trade-offs necessary in the choice of Aperture for 24mm landscapes.  The result of the process is a set of guidelines.  The answers are based on the previously introduced diffraction-aware model for sharpness in the center along the depth of the field – and a tripod-mounted Nikon Z7 + Nikkor 24-70mm/4 S kit lens at 24mm.
Continue reading DOF and Diffraction: 24mm Guidelines →

IQ, Optics, Perceptual, Sharpness, Spatial Resolution

DOF and Diffraction: Setup

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The two-thin-lens model for precision Depth Of Field estimates described in the last two articles is almost ready to be deployed.  In this one we will describe the setup that will be used to develop the scenarios that will be outlined in the next one.

The beauty of the hybrid geometrical-Fourier optics approach is that, with an estimate of the field produced at the exit pupil by an on-axis point source, we can generate the image of the resulting Point Spread Function and related Modulation Transfer Function.

Pretend that you are a photon from such a source in front of a f/2.8 lens focused at 10m with about 0.60 microns of third order spherical aberration – and you are about to smash yourself onto the ‘best focus’ observation plane of your camera.  Depending on whether you leave exactly from the in-focus distance of 10 meters or slightly before/after that, the impression you would leave on the sensing plane would look as follows:

Figure 1. PSF of a lens with about 0.6um of third order spherical aberration focused on 10m.

The width of the square above is 30 microns (um), which corresponds to the diameter of the Circle of Confusion used for old-fashioned geometrical DOF calculations with full frame cameras.  The first ring of the in-focus PSF at 10.0m has a diameter of about 2.44\lambda \frac{f}{D} = 3.65 microns.   That’s about the size of the estimated effective square pixel aperture of the Nikon Z7 camera that we are using in these tests.
Continue reading DOF and Diffraction: Setup →

Optics, Perceptual, Sharpness, Spatial Resolution

DOF and Diffraction: Image Side

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This investigation of the effect of diffraction on Depth of Field is based on a two-thin-lens model, as suggested by Alan Robinson[1].  We chose this model because it allows us to associate geometrical optics with one lens and Fourier optics with the other, thus simplifying the underlying math and our understanding.

In the last article we discussed how the front element of the model could present at the rear element the wavefront resulting from an on-axis source as a function of distance from the lens.  We accomplished this by using simple geometry in complex notation.  In this one we will take the relative wavefront present at the exit pupil and project it onto the sensing plane, taking diffraction into account numerically.  We already know how to do it since we dealt with this subject in the recent past.

Figure 1. Where is the plane with the Circle of Least Confusion?  Through Focus Line Spread Function Image of a lens at f/2.8 with the indicated third order spherical aberration coefficient, and relative measures of ‘sharpness’ MTF50 and Acutance curves.  Acutance is scaled to the same peak as MTF50 for ease of comparison and refers to my typical pixel peeping conditions: 100% zoom, 16″ away from my 24″ monitor.

Continue reading DOF and Diffraction: Image Side →

Optics, Perceptual, Sharpness

DOF and Diffraction: Object Side

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In this and the following articles we shall explore the effects of diffraction on Depth of Field through a two-lens model that separates geometrical and Fourier optics in a way that keeps the math simple, though via complex notation.  In the process we will gain a better understanding of how lenses work.

The results of the model are consistent with what can be obtained via classic DOF calculators online but should be more precise in critical situations, like macro photography.  I am not a macro photographer so I would be interested in validation of the results of the explained method by someone who is.

Figure 1. Simple two-thin-lens model for DOF calculations in complex notation.  Adapted under licence.

Continue reading DOF and Diffraction: Object Side →

IQ, Optics, Sharpness, Spatial Resolution

The Nikon Z7’s Insane Sharpness

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Ever since getting a Nikon Z7 MILC a few months ago I have been literally blown away by the level of sharpness it produces.   I thought that my surprise might be the result of moving up from 24 to 45.7MP, or the excellent pin-point focusing mode, or the lack of an Antialiasing filter.  Well, it turns out that there is probably more at work than that.

This weekend I pulled out the largest cutter blade I could find and set it up rough and tumble near vertically about 10 meters away  to take a peek at what the MTF curves that produce such sharp results might look like.

Continue reading The Nikon Z7’s Insane Sharpness →

IQ, Sensors, Sharpness, Spatial Resolution

Canon’s High-Res Optical Low Pass Filter

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Canon recently introduced its EOS-1D X Mark III Digital Single-Lens Reflex [Edit: and now also possibly the R5 Mirrorless ILC] touting a new and improved Anti-Aliasing filter, which they call a High-Res Gaussian Distribution LPF, claiming that

“This not only helps to suppress moiré and color distortion,
 but also improves resolution.”

Figure 1. Artist’s rendition of new High-res Low Pass Filter, courtesy of Canon USA

In this article we will try to dissect the marketing speak and understand a bit better the theoretical implications of the new AA.  For the abridged version, jump to the Conclusions at the bottom.  In a picture:

Canon High-Res Anti-Aliasing filter
Figure 16: The less psychedelic, the better.

Continue reading Canon’s High-Res Optical Low Pass Filter →

Deconvolution, IQ, Optics, Sharpening, Sharpness, Spatial Resolution

Capture Sharpening: Estimating Lens PSF

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The next few articles will outline the first tiny few steps towards achieving perfect capture sharpening, that is deconvolution of an image by the Point Spread Function (PSF) of the lens used to capture it.  This is admittedly  a complex subject, fraught with a myriad ever changing variables even in a lab, let alone in the field.  But studying it can give a glimpse of the possibilities and insights into the processes involved.

I will explain the steps I followed and show the resulting images and measurements.  Jumping the gun, the blue line below represents the starting system Spatial Frequency Response (SFR)[1], the black one unattainable/undesirable perfection and the orange one the result of part of the process outlined in this series.

Figure 1. Spatial Frequency Response of the imaging system before and after Richardson-Lucy deconvolution by the PSF of the lens that captured the original image.

Continue reading Capture Sharpening: Estimating Lens PSF →

Color, IQ, Sharpness, Spatial Resolution

Bayer CFA Effect on Sharpness

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In this article we shall find that the effect of a Bayer CFA on the spatial frequencies and hence the ‘sharpness’ information captured by a sensor compared to those from the corresponding monochrome version can go from (almost) nothing to halving the potentially unaliased range – based on the chrominance content of the image and the direction in which the spatial frequencies are being stressed. Continue reading Bayer CFA Effect on Sharpness →

Optics, Quantization, Sensors, Spatial Resolution

Wavefront to PSF to MTF: Physical Units

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In the last article we saw that the intensity Point Spread Function and the Modulation Transfer Function of a lens could be easily approximated numerically by applying Discrete Fourier Transforms to its generalized exit pupil function \mathcal{P} twice in sequence.[1]

Numerical Fourier Optics: amplitude Point Spread Function, intensity PSF and MTF

Obtaining the 2D DFTs is easy: simply feed MxN numbers representing the two dimensional complex image of the Exit Pupil function in its uv space to a Fast Fourier Transform routine and, presto, it produces MxN numbers representing the amplitude of the PSF on the xy sensing plane.  Figure 1a shows a simple case where pupil function \mathcal{P} is a uniform disk representing the circular aperture of a perfect lens with MxN = 1024×1024.  Figure 1b is the resulting intensity PSF.

Figure 1a, left: A circular array of ones appearing as a white disk on a black background, representing a circular aperture. Figure 1b, right: Array of numbers representing the PSF of image 1a in the classic shape of an Airy Pattern.
Figure 1. 1a Left: Array of numbers representing a circular aperture (zeros for black and ones for white).  1b Right: Array of numbers representing the PSF of image 1a (contrast slightly boosted).

Simple and fast.  Wonderful.  Below is a slice through the center, the 513th row, zoomed in.  Hmm….  What are the physical units on the axes of displayed data produced by the DFT? Continue reading Wavefront to PSF to MTF: Physical Units →

Optics, Photometry, Quantization, Radiometry, Sensors, Spatial Resolution

Aberrated Wave to Image Intensity to MTF

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Goodman, in his excellent Introduction to Fourier Optics[1], describes how an image is formed on a camera sensing plane starting from first principles, that is electromagnetic propagation according to Maxwell’s wave equation.  If you want the play by play account I highly recommend his math intensive book.  But for the budding photographer it is sufficient to know what happens at the Exit Pupil of the lens because after that the transformations to Point Spread and Modulation Transfer Functions are straightforward, as we will show in this article.

The following diagram exemplifies the last few millimeters of the journey that light from the scene has to travel in order to be absorbed by a camera’s sensing medium.  Light from the scene in the form of  field  U arrives at the front of the lens.  It goes through the lens being partly blocked and distorted by it as it arrives at its virtual back end, the Exit Pupil, we’ll call this blocking/distorting function P.   Other than in very simple cases, the Exit Pupil does not necessarily coincide with a specific physical element or Principal surface.[iv]  It is a convenient mathematical construct which condenses all of the light transforming properties of a lens into a single plane.

The complex light field at the Exit Pupil’s two dimensional uv plane is then  U\cdot P as shown below (not to scale, the product of the two arrays is element-by-element):

Figure 1. Simplified schematic diagram of the space between the exit pupil of a camera lens and its sensing plane. The space is assumed to be filled with air.

Continue reading Aberrated Wave to Image Intensity to MTF →

IQ, Optics, Sharpness, Spatial Resolution

Taking the Sharpness Model for a Spin – II

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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:

Table 1. The cameras and lenses under test.

Continue reading Taking the Sharpness Model for a Spin – II →

Optics, Sharpness, Spatial Resolution

Taking the Sharpness Model for a Spin

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The series of articles starting here outlines a model of how the various physical components of a digital camera and lens can affect the ‘sharpness’ – that is the spatial resolution – of the  images captured in the raw data.  In this one we will pit the model against MTF curves obtained through the slanted edge method[1] from real world raw captures both with and without an anti-aliasing filter.

With a few simplifying assumptions, which include ignoring aliasing and phase, the spatial frequency response (SFR or MTF) of a photographic digital imaging system near the center can be expressed as the product of the Modulation Transfer Function of each component in it.  For a current digital camera these would typically be the main ones:

(1)   \begin{equation*} MTF_{sys} = MTF_{lens} (\cdot MTF_{AA}) \cdot MTF_{pixel} \end{equation*}

all in two dimensions Continue reading Taking the Sharpness Model for a Spin →

Optics, Sharpness, Spatial Resolution

A Simple Model for Sharpness in Digital Cameras – Polychromatic Light

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We now know how to calculate the two dimensional Modulation Transfer Function of a perfect lens affected by diffraction, defocus and third order Spherical Aberration  – under monochromatic light at the given wavelength and f-number.  In digital photography however we almost never deal with light of a single wavelength.  So what effect does an illuminant with a wide spectral power distribution, going through the color filter of a typical digital camera CFA  before the sensor have on the spatial frequency responses discussed thus far?

Monochrome vs Polychromatic Light

Not much, it turns out. Continue reading A Simple Model for Sharpness in Digital Cameras – Polychromatic Light →

Optics, Sharpness, Spatial Resolution

A Simple Model for Sharpness in Digital Cameras – Spherical Aberrations

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Spherical Aberration (SA) is one key component missing from our MTF toolkit for modeling an ideal imaging system’s ‘sharpness’ in the center of the field of view in the frequency domain.  In this article formulas will be presented to compute the two dimensional Point Spread and Modulation Transfer Functions of the combination of diffraction, defocus and third order Spherical Aberration for an otherwise perfect lens with a circular aperture.

Spherical Aberrations result because most photographic lenses are designed with quasi spherical surfaces that do not necessarily behave ideally in all situations.  For instance, they may focus light on systematically different planes depending on whether the respective ray goes through the exit pupil closer or farther from the optical axis, as shown below:

371px-spherical_aberration_2
Figure 1. Top: an ideal spherical lens focuses all rays on the same focal point. Bottom: a practical lens with Spherical Aberration focuses rays that go through the exit pupil based on their radial distance from the optical axis. Image courtesy Andrei Stroe.

Continue reading A Simple Model for Sharpness in Digital Cameras – Spherical Aberrations →

Optics, Sharpness, Spatial Resolution

A Simple Model for Sharpness in Digital Cameras – Defocus

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This series of articles has dealt with modeling an ideal imaging system’s ‘sharpness’ in the frequency domain.  We looked at the effects of the hardware on spatial resolution: diffraction, sampling interval, sampling aperture (e.g. a squarish pixel), anti-aliasing OLPAF filters.  The next two posts will deal with modeling typical simple imperfections related to the lens: defocus and spherical aberrations.

Defocus = OOF

Defocus means that the sensing plane is not exactly where it needs to be for image formation in our ideal imaging system: the image is therefore out of focus (OOF).  Said another way, light from a point source would go through the lens but converge either behind or in front of the sensing plane, as shown in the following diagram, for a lens with a circular aperture:

Figure 1. Back Focus, In Focus, Front Focus.
Figure 1. Top to bottom: Back Focus, In Focus, Front Focus.  To the right is how the relative PSF would look like on the sensing plane.  Image under license courtesy of Brion.

Continue reading A Simple Model for Sharpness in Digital Cameras – Defocus →

Quantization, Sensors, Spatial Resolution

The Units of Discrete Fourier Transforms

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This article is about specifying the units of the Discrete Fourier Transform of an image and the various ways that they can be expressed.  This apparently simple task can be fiendishly unintuitive.

The image we will use as an example is the familiar Airy Pattern from the last few posts, at f/16 with light of mean 530nm wavelength. Zoomed in to the left in Figure 1; and as it looks in its 1024×1024 sample image to the right:

Airy Mesh and Intensity
Figure 1. Airy disc image I(x,y). Left, 1a, 3D representation, zoomed in. Right, 1b, as it would appear on the sensing plane (yes, the rings are there but you need to squint to see them).

Continue reading The Units of Discrete Fourier Transforms →

IQ, Optics, Sensors, Sharpness, Spatial Resolution

A Simple Model for Sharpness in Digital Cameras – Sampling & Aliasing

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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 with 100% Fill Factor we now turn to the effect of the sampling interval on spatial resolution according to the guiding formula:

(1)   \begin{equation*} MTF_{Sys2D} = \left|(\widehat{ PSF_{lens} }\cdot \widehat{PIX_{ap} })\right|_{pu}\ast\ast\: \delta\widehat{\delta_{pitch}} \end{equation*}

The hats in this case mean the Fourier Transform of the relative component normalized to 1 at the origin (_{pu}), that is the individual MTFs of the perfect lens PSF, the perfect square pixel and the delta grid;  ** represents two dimensional convolution.

Sampling in the Spatial Domain

While exposed a pixel sees the scene through its aperture and accumulates energy as photons arrive.  Below left is the representation of, say, the intensity that a star projects on the sensing plane, in this case resulting in an Airy pattern since we said that the lens is perfect.  During exposure each pixel integrates (counts) the arriving photons, an operation that mathematically can be expressed as the convolution of the shown Airy pattern with a square, the size of effective pixel aperture, here assumed to have 100% Fill Factor.  It is the convolution in the continuous spatial domain of lens PSF with pixel aperture PSF shown in Equation (2) of the first article in the series.

Sampling is then the product of an infinitesimally small Dirac delta function at the center of each pixel, the red dots below left, by the result of the convolution, producing the sampled image below right.

Footprint-PSF3
Figure 1. Left, 1a: A highly zoomed (3200%) image of the lens PSF, an Airy pattern, projected onto the imaging plane where the sensor sits. Pixels shown outlined in yellow. A red dot marks the sampling coordinates. Right, 1b: The sampled image zoomed at 16000%, 5x as much, because in this example each pixel’s width is 5 linear units on the side.

Continue reading A Simple Model for Sharpness in Digital Cameras – Sampling & Aliasing →

Optics, Sensors, Sharpness, Spatial Resolution

A Simple Model for Sharpness in Digital Cameras – Diffraction and Pixel Aperture

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Now that we know from the introductory article that the spatial frequency response of a typical perfect digital camera and lens (its Modulation Transfer Function) can be modeled simply as the product of the Fourier Transform of the Point Spread Function of the lens and pixel aperture, convolved with a Dirac delta grid at cycles-per-pixel pitch spacing

(1)   \begin{equation*} MTF_{Sys2D} = \left|\widehat{ PSF_{lens} }\cdot \widehat{PIX_{ap} }\right|_{pu}\ast\ast\: \delta\widehat{\delta_{pitch}} \end{equation*}

we can take a closer look at each of those components (pu here indicating normalization to one at the origin).   I used Matlab to generate the examples below but you can easily do the same with a spreadsheet.   Continue reading A Simple Model for Sharpness in Digital Cameras – Diffraction and Pixel Aperture →

IQ, MTF, Perceptual, PSF, Spatial Resolution, spectral response

COMBINING BAYER CFA MTF Curves – II

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In this and the previous article I discuss how Modulation Transfer Functions (MTF) obtained from the raw data of each of a Bayer CFA color channel can be combined to provide a meaningful composite MTF curve for the imaging system as a whole.

There are two ways that this can be accomplished: an input-referred approach (L) that reflects the performance of the hardware only; and an output-referred one (Y) that also takes into consideration how the image will be displayed.  Both are valid and differences are typically minor, though the weights of the latter are scene, camera/lens, illuminant dependent – while the former are not.  Therefore my recommendation in this context is to stick with input-referred weights when comparing cameras and lenses.1 Continue reading COMBINING BAYER CFA MTF Curves – II →

Deconvolution, IQ, Sharpening, Spatial Resolution

Downsizing Algorithms: Effects on Resolution

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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.

Continue reading Downsizing Algorithms: Effects on Resolution →

Equivalence, Formats, IQ, Spatial Resolution

Are micro Four Thirds Lenses Typically Twice as ‘Sharp’ as Full Frame’s?

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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.

Continue reading Are micro Four Thirds Lenses Typically Twice as ‘Sharp’ as Full Frame’s? →

Spatial Resolution

MTF Mapper vs sfrmat3

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Over the last couple of years I’ve been using Frans van den Bergh‘s excellent open source MTF Mapper to measure the Modulation Transfer Function of imaging systems off a slanted edge target, as you may have seen in these pages.  As long as one understands how to get the most out of it I find it a solid product that gives reliable results, with MTF50 typically well within 2% of actual in less than ideal real-world situations (see below).  I had little to compare it to other than to tests published by gear testing sites:  they apparently mostly use a commercial package called Imatest for their slanted edge readings – and it seemed to correlate well with those.

Then recently Jim Kasson pointed out sfrmat3, the matlab program written by Peter Burns who is a slanted edge method expert who worked at Kodak and was a member of the committee responsible for ISO12233, the resolution and spatial frequency response standard for photography.  sfrmat3 is considered to be a solid implementation of the standard and many, including Imatest, benchmark against it – so I was curious to see how MTF Mapper 0.4.1.6 would compare.  It did well.

Continue reading MTF Mapper vs sfrmat3 →

Equivalence, Formats, IQ, Sensors, Spatial Resolution

Olympus E-M5 II High-Res 64MP Shot Mode

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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.  Preliminary tests show that the E-M5 mk II 64MP High-Res mode gives some advantage in MTF50 linear spatial resolution compared to the Standard Shot 16MP mode with the captures in this post.  Plus it apparently virtually eliminates the possibility of  aliasing and moiré.  Great stuff, Olympus.

Continue reading Olympus E-M5 II High-Res 64MP Shot Mode →

Equivalence, IQ, Optics, Sensors, Spatial Resolution

The Units of Spatial Resolution

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Several sites for photographers perform spatial resolution ‘sharpness’ testing of a specific lens and digital camera set up by capturing a target.  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 popular slanted edge method, although their applicability is generic.

Continue reading The Units of Spatial Resolution →

IQ, Spatial Resolution

How to Get MTF Performance Curves for Your Camera and Lens

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You have obtained a raw file containing the image of a slanted edge  captured with good technique.  How do you get the Modulation Transfer Function of the camera and lens combination that took it?  Download and feast your eyes on open source MTF Mapper version 0.4.16 by Frans van den Bergh.

[Edit, several years later: MTF Mapper has kept improving over time, making it in my opinion the most accurate slanted edge measuring tool available today, used in applications that range from photography to machine vision to the Mars Rover.   Did I mention that it is open source?

It now sports a Graphical User Interface which can load raw files and allow the arbitrary selection of individual edges by simply pointing and clicking, making this post largely redundant.  The procedure outlined will still work but there are easier ways to accomplish the same task today.  To obtain the same result with raw data and version 0.7.38 just install MTF Mapper, set the “Settings/Preferences” tab as follows and leave all else at default:

“Pixel size” is only needed to also show SFR in units of lp/mm and the “Arguments” field only if using an unspecified raw data CFA layout.  “Accept” and “File/Open with manual edge selection” your raw files.  Follow the instructions to select as many edges as desired.  Then in “Data set” open an “annotated” file and shift-click on the chosen edges to see the relative MTF plots.]

The first thing we are going to do is crop the edges and package them into a TIFF file format so that MTF Mapper has an easier time reading them.  Let’s use as an example a Nikon D810+85mm:1.8G ISO 64 studio raw capture by DPReview so that you can follow along if you wish.   Continue reading How to Get MTF Performance Curves for Your Camera and Lens →

IQ, Optics, Sharpness, Spatial Resolution

The Slanted Edge Method

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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 more, useful, accurate, quantitative 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 camera/lens system impulse response – at the location of the edge in the direction perpendicular to it.

Much of what there is to know about an imaging system’s spatial resolution performance can be deduced by analyzing its MTF curve, which represents the system’s ability to capture increasingly fine detail from the scene, starting from perceptually relevant metrics like MTF50, discussed a while back.

In fact the area under the curve weighted by some approximation of the Contrast Sensitivity Function of the Human Visual System is the basis for many other, better accepted single figure ‘sharpness‘ metrics with names like Subjective Quality Factor (SQF), Square Root Integral (SQRI), CMT Acutance, etc.   And all this simply from capturing the image of a slanted edge, which one can actually and somewhat easily do at home, as presented in the next article.

Continue reading The Slanted Edge Method →

IQ, Perceptual, Sharpening, Spatial Resolution

Why Raw Sharpness IQ Measurements Are Better

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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.

Can we do that off a file rendered by a raw converter or, heaven forbid, a Jpeg?  Not quite, especially if the objective is measuring IQ. Continue reading Why Raw Sharpness IQ Measurements Are Better →

IQ, Perceptual, Sharpening, Spatial Resolution

How Sharp are my Camera and Lens?

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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:

  1. The setup (this one)
  2. Why you need to take raw captures
  3. The Slanted Edge method explained
  4. The software to obtain MTF curves

Continue reading How Sharp are my Camera and Lens? →

Perceptual, Sharpness, Spatial Resolution

MTF50 and Perceived Sharpness

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Is MTF50 a good proxy for perceived sharpness?   In this article and those that follow MTF50 indicates the spatial frequency at which the Modulation Transfer Function of an imaging system is half (50%) of what it would be if the system did not degrade detail in the image painted by incoming light.

It makes intuitive sense that the spatial frequencies that are most closely related to our perception of sharpness vary with the size and viewing distance of the displayed image.

For instance if an image captured by a Full Frame camera is viewed at ‘standard’ distance (that is a distance equal to its diagonal), it turns out that the portion of the MTF curve most representative of perceived sharpness appears to be around MTF90.  On the other hand, when pixel peeping the spatial frequencies around MTF50 look to be a decent, simple to calculate indicator of it, assuming a well set up imaging system in good working conditions. Continue reading MTF50 and Perceived Sharpness →