A Study of Slanted-Edge MTF Stability and Repeatability
Jackson K.M.Roland
Imatest LLC,2995Wilderness Place Suite103,Boulder,CO,USA
ABSTRACT
The slanted-edge method of measuring the spatial frequency respon(SFR)as an approximation of the mod-
ulation transfer function(MTF)has become a well known and widely ud image quality testing method over
the last10years.This method has been adopted by multiple international standards including ISO and IEEE.
Nearly every commercially available image quality testing software includes the slanted-edge method and there环球雅思学费
are numerous open-source algorithms available.This method is one of the most important image quality algo-
rithms in u today.This paper explores test conditions and the impacts they have on the stability and precision英语46级成绩查询
of the slanted-edge method as well as details of the algorithm itlf.Real world and simulated data are ud
to validate the characteristics of the algorithm.Details of the target such as edge angle and contrast ratio are
tested to determine the impact on measurement under various conditions.The original algorithm defines a near
vertical edge so that errors introduced are minor but the theory behind the algorithm requires a perfectly vertical
edge.A correction factor is introduced as a way to compensate for this problem.Contrast ratio is shown to have
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no impact on results in an abnce of noi.
Keywords:MTF,SFR,slanted edge,image quality,sharpness
1.INTRODUCTION
The slanted-edge method of measuring the spatial frequency respon(SFR)as an approximation of the mod-
ulation transfer function(MTF)has become a well known and widely ud image quality testing method over
the last10years.This method has been adopted by multiple international standards including ISO and IEEE.1
Nearly every commercially available image quality testing software includes the slanted-edge method and there
are numerous open-source algorithms available.This method is easily one of the most important image quality
algorithms in u today.
The algorithm itlf has remained relatively unchanged since it’s original publication in ISO12233:2000.2
Despite the consistency of the algorithm,in the latest2014revision of the ISO12233standard there was a major
modification to the recommended target.In the original2000edition of ISO12233the target was required to
have a minimum edge contrast of40:1.The revid standard specifies the edge contrast to be4:1.3This change
国家承认的自考本科reflects a change in understanding of the slant edge measurement,with high contrast the measurement becomes
unstable and so the contrast was lowered.The standard also defines a5 slanted edge rather than another edge angle.There is very little published evidence as to why the specifications are made for the slanted-edge
measurement.This rais a question,how stable is the slanted-edge method and under what testing conditions
will it be most stable?名声大噪
que ra ra歌词Mathematically there are veral known limitations of the slanted-edge algorithm.First and foremost is
the angle of the the edge being measured relative the the nsor array.The relative edge angle must not be
at n⇡
4increments where n is an integer value.Should the angle fall on one of the“whole angle”increments
the algorithm will be missing frequency information that is calculated from the pha-o↵t portions of an edge relative to the nsor.This paper builds on the work done by Peter Burns4and Don Williams5to help characterize targets and environments.
Further author information:(Send correspondence to J.K.M.R)
J.K.M.R:E-mail:,Telephone:+19706928273
Table 1:Real-world data t variables Variable Values Edge Angle 5,10,15Contrast Ratio 1.4,2.1,4.3,4.8,11.3,33.7ISO Speed 100,400,1600,6400
2.EXPERIMENTAL
2.1Capture
In order to validate that simulated edge regions can be ud,a data t was acquired from a Canon EOS 6D of a ries of slanted edges.The camera was t up on a stable tripod at a distance of 190cm from the targets.The targets were illuminated with 4000K illumination at 355
lux with a uniformity of 95%across the measured field.职称英语报名入口
人力资源管理师三级Figure 1:Diagram of lighting tup
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A ries of images was acquired across a range of slanted edge angles,contrast,and noi levels (See Table 1).The contrast level and edge angle was varied by switching out targets.The noi level was varied by changing the ISO nsitivity of the camera.The exposure was kept constant by varying the shutter speed inverly to the ISO nsitivity.
The lens model ud to capture the data t was a Canon EF 24-70mm f /4L IS USM t to an aperture of f /5.6and a focal length of 70mm.Manual focus was t and maintained for all images captured.The data t was captured in CR2uncompresd raw and large,max quality JPEG formats and for each variable combination 10images were captured.The raw image files were converted to linear TIFF files for processing,removing gamma encoding as a variable.
2.2Data Processing
The algorithm ud to calculate the slanted-edge MTF for all results is a modified version of the ISO standard.The version ud here included a noi reduction process on non-edge areas of the region
and a cond-order fit to the edge instead of a first-order fit.Overall this has reduced the variability prent in the results,however the relative di ↵erences remain constant.A follow-up study is planned to show the preci impact of the changes on results.
Table 2:Reported slanted-edge results
MTF50MTF30Light Mean Pixel Value Dark Mean Pixel Value Edge Angle
Figure2:Mean MTF plot and edge profile for ISO100,5 Edge Angle,4.3:1Contrast data t
A region was lected that would be of a reasonable size and would cover the edge in all images.The metrics shown in Table2were reported along with the MTF curve out to just past the Nyquist frequency and the edge profile(See Figure2).
For each reported result the mean and standard deviation was calculated across all10images in each variable t.An example of thefinal reported data is shown in Table3.
Table3:Example of results for ISO100,5 Edge Angle,4.3:1Contrast data t
Result Mean Std.Dev.
MTF500.2300.013
MTF300.3170.018
Light Mean32.1590.065
Dark Mean 6.7400.019
Edge Angle 4.6350.002
3.SIMULATED DATA GENERATION
In order to expand the range of testing without having a monumental task of data acquisition,a simulated data t was generated to correlate with the real-world data t.Two simulated data ts were generated:One to match the design of the real-world data t varying similar values and one to cover a much wider range of variables.All data was generated using a MATLAB anti-aliad edge generator which applied an Gaussian-bad simulated point spread function(PSF).All noi added to the simulated edges was standard Gaussian noi with a zero-mean and constant variance.
Figure3:Example simulated5 edge with no noi
(a)MTF50in cycles per pixel plotted as a function of detected edge angle (b)Standard deviation of MTF50plotted as a function
常用英语900句
of detected edge angle
Figure 4:Plots for real world results
4.RESULTS
4.1Real World Data
The real world data ts allow us to show the approximate variability under certain circumstances and to estimate the e ↵ect of certain variables when compared to simulated data.The full data t shows some interesting aspects of the camera itlf in addition to the more general aspects.Figure 4shows that despite the raw images and lack of signal processing,the camera gave systematically lower results at ISO 1600compared to the higher noi ISO 6400.It also shows that,as might be expected,the highest ISO and likely highest noi had the greatest variability and most outliers.Ignoring the outliers however,the edge angle estimation remains very accurate at all target angles and all noi levels.Furthermore the variability within an noi level remain very similar at all edge angles with no obvious systematic change.Contrast appears to have little e ↵ect on real world data that is outside the variability caud by noi.
Edge angle does appear to have an impact on variability in some systems however.At ISO 100the variability of MTF50clearly increas with edge angle.Since this does not em to occur at any other noi level it is possible that this an artifact of the signal processing in the camera.Further study is needed to determine if this is the ca.
Figure 5shows the e ↵ect of contrast ratio on the real world data t.Generally the lower contrast ratios have a lower MTF50.This can primarily be expected bad on the noi,however an examination of the noi does not fully support this assumption.More study of the results is required and may be discusd in a future paper.
Figure 5:MTF50in cycles per pixel plotted as a function of contrast ratio and colored by ISO of the data t with linear trendlines
Figure 6:Simulated contrast data t with varying contrast and constant edge angle
4.2Contrast
Given that the contrast ratio change is the only significant change made to standards using the slanted-edge calculation in the last 10years this will be the first issue we look at here.Since the images are completely simulated and there is no radiometric data to associate with the pixel values,it is assumed that the files have a gamma of 1.0.It is also assumed that the simulated values,for the purpos of determining relative contrast of the edge,directly correspond to luminance (Y)values from CIE XYZ (e.g.255pixel =1.0Y).
As en in Figure 7,the MTF50remained extremely stable across all contrast levels with no noi prent.The overall standard deviation in the MTF50was less than 0.075%.Statistically speaking,the results are absolutely equivalent.
However the measurements were made in an abnce of noi.When significant noi is prent the contrast does gain certain importance.Figure 8shows the MTF50across the same t of contrast ratios with simulated noi with a sigma of 0.001applied.The lowest contrast (1.1:1)clearly indicates a failed measurement.The addition of the noi was enough to bring the signal to noi ratio so low t
hat the edge was undetectable.Leaving the outlier of the lowest contrast ratio,the remaining contrasts show e ↵ectively the same results as the edges with no noi.The overall standard deviation is higher (2.0%)but this is within the variability created by the noi itlf.
4.3Angle
The well described theory behind the slanted-edge MTF measurement 6,7explains that the reason behind slanting the edge is to get pha o ↵ts in di ↵erent cross-ctions of the same edge.The pha o ↵ts are ud to calculated an oversampled edge profile,allowing for detection of frequencies near and above Nyquist.Ideally,the slanted edge would only be slanted enough to pass across a minimum number of sampling sites (pixels)to get
Figure 7:MTF50in cycles per pixel across multiple simulated contrast ranges (See Figure 6)
