来源：http://michel.thoby.free.fr/Fisheye_history_short/International_Standards_about_Distortion.html
How is lens distortion value being defined by the industry and by some International Standardization Groups?
Foreword:
There are many "Standards" (e.g. Industrial and International and dealing somewhat with distortion) that are around and there are many. While some of these Standards are now obsolete and while other Standards are still on the works, they yet seem to be applied somehow by somebody somewhere whilst most are infortunately conflicting with each others.
A revision of the ISO 9039-1994 was released in 2008 to cope with the recent and rapid changes in the industry: ISO 9039-2008 "Optics and photonics -Quality evaluation of optical systems -Determination of distortion" (Optique et photonique -Evaluation de la qualilté des systèmes - Détermination de la distorsion). DXO for instance, claims to be actively supporting this new ISO Standard (read "Le Photographe" magazine #1675, Jul-Aug 2009, page 81) but we were deeply disappointed to find that in fact they do not apply that Standard in any way and worse: some of their popular published data are conflicting with this Standard!
1- Standard Mobile Imaging Architecture (SMIA)
The test analyses by some reviewers (e.g. Imatest) were done by using SMIA standards.
The documentation is rather hard to get nowadays. It seems that the project has folded. We could not find a sign of life on the web and I3A (see below) seems to have taken precedence over the SMIA initiative when I3A sarted in 2006 the so-called Camera Phone Image Quality (CPIQ) initiative.We would appreciate to hear the clear story told by knowledgeable insiders on this subject.
Ref: Image sensor characterization using Standard Mobile Imaging Architecture (SMIA) standard by NICOL Robert L.
and SMIA 1.0 Part 2: CCP2 Specification SMIA 1.0 Part 5: Camera Characterisation Specification Rev A; §5.20 = TV Distortion
2-Traditional definition of (TV) distortion (e.g. by European Broadcasting Union)
EBU_Distortion_Figure.jpg
Hence the relative PHD or TV distortionvalue shall be about twice the SMIA TV distortion.
Note: Imatest follows SMIA Standards. One can read on a imatest page the following remark:
<< SMIA vs. traditional TV distortion
.... SMIA's distortion definition differs from the traditional TV industry definition by a factor of two. The traditional definition is shown in the following illustration, which has been adapted from the publication "Optical Terms," published by Fujinon. The same definition appears in "Measurement and analysis of the performance of film and television camera lenses" published by the European Broadcasting Union (EBU). SMIA TV distortion is double the traditional TV distortion definition.
Imatest will continue to use the SMIA definition, which has been widely adopted in the mobile imaging industry. We prefer it because it is self-consistent. In the traditional definition, TV distortion is the change (Δ) in the center-to-top distance divided by by the bottom-to-top distance. In the SMIA definition, both A and B are bottom-to-top distances.>>
3-Image Engineering (Germany)
Image Engineering.de (IE) is based in Germany. On its catalogue cover sheet, the reader is said to be able to find "Solutions for best imageQuality". Besides hundreds of test charts, IE sell software modules for optical system testing and among those modules, a "Distortion" module that enables the user to evaluate the distortion and the lateral chromatic aberration in one step. The outputted results are
- TV distortion (EBU, SMIA)
- lens geometric distortion
- 2D and vector plot for distortion
On the conclusion of a paper about "Three Years of Practical Experience in Using ISO Standards for Testing Digital Cameras", Christian Loebich and Dietmar Wueller wrote in 2000: Right now we are working on measuring parameters like lens distortion. Much later, on their White Paper IE give more details and write: << The distortion shall be measured as SMIA TV distortion in wide angle position as the bending of a horizontal line on the top and bottom of the image in relation to the image height as specified in the SMIA 13 specification, §5.20>>. In 2006, Dietmar Wueller reiterated the IE support to the SMIA standard for quantifying "distortion" in the article titled "Proposal for a Standard Procedure to Test Mobile Phone Cameras".
IE have posted the User's manual for their IE Analyzer tool. An extract of the page 108 of the IE Analyzer manual is as follows and very clearly shows that they measure distortion value similar to SMIA:
BTW: IE apparently are not involved in development or sale of software for Image post-processing and correction. They also seem to not being recently active in showing Cameras sensitivity or lenses quality.
4-DXO Labs
DXO announced and introduced DXO Analyzer at the P.M.A. in February 200. From March 2004on, the french magazine "Chasseurs d'images" uses DXO Analyzer in its its C.I.Lab (formerly called C.E.C.I.). The competition followed soon and" Le Photographe"," Réponses Photo", "Popular Photography", "Nippon Camera", "Digital Photo","Pictchallenge.com", "Le monde de la photo.com","LuminousLandscape.com" Bench Expert, FNAC and DIWA Labs (just to name a few), all were then issuing lens test results from using DXO test means.
Of course, DXOMark uses its own product (i.e.DXO Analyzer).
DXO Labs claim to apply both SMIA and ( I3A) Industry Standards but this appears to be not the case at least as lens geometric (radial) distortion is concerned. They have adopted yet another different way to define distortion:
<< Distortion is characterized by measuring the positional errors associated with a series of points that are aligned on a test target (but not necessarily aligned in the image because of the distortion) according to the following procedure: Computation of the largest distance (l) between points that should belong to the same straight line and the straight line defined by the two points located at its ends (separated by a distance, L); The positional error measurement related to this series of points is the ratio l/L, expressed as a percentage (since it is a distance ratio)>>
In addition the sign of the distortion figure is reversed when compared with all other Standards We could not think of a valid reason for this strange inversion as DxOLabs knows about this. Here follow extracts from two different papers that were written by DxOLabs (both having the very same illustrations and images shown on them) :
|
"Information capacity: a measure of potential image quality of a digital camera" This paper from DxOLabs was published at Electronic Imaging (January 17-21, 2010 – San Jose, California, USA) |
On their DXOMark site, the presentation of Distortion by DxOLabs is illustrated with the same images as on the paper related at the left of this table, but here... the sign is reversed |
| 4.4 Lens distortion Lens distortion is another field aberration that implies that lens magnification varies in the image field. The major consequence of distortion is that straight lines in the scene appear curved in the image(.....). For certain lenses, distortion can depend on the distance to the scene, making the correction a bit inaccurate. (....). Consider first the case of negative distortion, also called barrel distortion on Fig. (2). (....) Conversely, for positive (or pincushion) distortion (Figure 3), |
What is distortion? (...) For DSLR lenses, this aberration has a radial symmetry. (....) Two types of distortion may arise: Barrel distortion, in which the grid takes the form of a barrel (lines near the edges bend outwards). (....) Pincushion distortion, in which the grid takes the form of a pincushion (lines near the edges bend inwards). (....) Complex lenses can actually show a mix of these two behaviors. A zoom lens can exhibit one type of distortion at one end of the zoom range and the other type at the other end of the range. (....) The value is positive in the case of barrel distortion, and negative in the case of pincushion distortion. It is null when there is no distortion. |
| Additional note by this author: because of the philosophy that DXO has adopted, a hefty moustache type of distortion may well be metered as ZERO | |
While one can read For DSLR lenses, this aberration has a radial symmetry, the definition of distortion by DXO "seems" not to take into account the rotational symetry of the photographic optical systems: in their presentation and their way to measure distortion, the longitudinal optical axis is not the reference axis and the Principal Point (that is usually the center of the image coordinate systems) is never retained as such on their presentations to the public: the distortion is not represented as being radially affecting the image geometry: they call it "Lateral Distortion" and interrestingly describe it as "a field aberration that implies that lens magnification varies in the image field. DXO presents the geometrical aberration as a defect on the rectangular image (i.e. a "straight line" must be to be corrected to become straight) rather than an optical defect of a rotational symetrical lens (i.e. that varies with the distance from the center of the image).
In short: as they divide by the length of the line (when the preceeding authors divided by the hight of the figure) the way that DXO computes distortion level yields values that are about 1.5 less than the traditional definition when dealing with images with a 3:2 ratio (APS-C or 24 x36 mm).
REMARKS:
- The french magazine "Réponse Photo" puts the DXO Analzer logo on their graphs but strangely the result range for distortion seems somewhat unrealistic if they were performed and analyzed with DxO Analyzer as some lens would suffer from distortion about 4 to 6 times the normal level measured by others also with the same DXO test means! Ques Aquo?
- DPReview.com have invented another rather fancy way to present distortion. They are quoting 2 values in the Data pannel below the grid representation and the sign of the distortion value is "à la DXO" i.e. positive for a barrel type of distortion. Along with the grid representation, they present three results in the data panel:
-
Short edge: defined as the percentage difference in length between the central vertical grid line and the left/right ‘short edge’. Describes the degree of bowing of the upper and lower horizontal lines, which are normally the most distorted.
-
Long edge: defined as the percentage difference in length between the central horizontal grid line and the top/bottom ‘long edge’. Describes the degree of bowing of the outermost left and right vertical lines.
- Distortion type: Barrel or pincushion >>
The computation for "short edge" is apparently similar to the SMIA standard while the "large edge" resembles the DxO's way !
Unfortunately, in real life many lenses have the most distorted line away from the upper and lower lines though and finding the distortion near the edge in fact doesn't give the "maximum" distortion.
International Imaging Industry Association (a.k.a. I3A)
I3A is actively contributing to the ISO Standards. However the most conspicuous endeavor by I3A is the CPIQ: The International Imaging Industry Association (I3A) launched the Camera Phone Image Quality (CPIQ) Initiative in June 2006. The goal of this initiative was to develop an image quality testing and performance rating system that could enable manufacturers and carriers to make comparisons between capture devices, and to communicate a substantiated product quality rating to consumers. The participating companies include wireless network operators, wireless device vendors, camera module manufacturers, camera component manufacturers, and image services providers. It seems that Distortion metrics have not amongst the main priority of the effort whreas objective metric forColor Uniformity for example, is described as the most urgent subject, not distortion.
I3A is possibly leaning toward DXO views. As an example one can read the press release issued by DXO when he announced DXO Analyzer 4. Following is an exerpt: <<While developing its testing tools, DxO Labs has been working closely with international organizations to validate its technology and incorporate it into standardization efforts.
According to Lisa Walker, president of I3A (the International Imaging Industry Association), “DxO Labs has been a major contributor to the standardization of cameraphone image quality evaluation undertaken by I3A over the past several years. DxO Labs has proposed innovative methods to address the challenge of developing objective metrics for important image quality attributes, which the CPIQ (Camera Phone Image Quality) team has successfully correlated with consumer perception. In particular, DxO Labs’ approaches to measuring texture preservation, distortion, chromatic aberration, and color shading have been the foundation for CPIQ participants to build toward our goals.”>>
Adobe systems
Adobe has also separately developped a tool LPC (Lens Profile Creator) that also measures geometric lens distortion. But at the time of writting this article, Adobe has not shown intention to publish any lens distortion value albeit they could do so. They have not to adopt a definition for distortion: the Adobe LPC (free and open) set of tools is only for correcting the image aberrations and not for providing quality metrics. BTW when doing so, they directly compete with DXO that also sells "DXO Optics Pro" with specific modules to photographers in order to correct images of Camera + Lens specific combos! Most of the Camera manufacturers give or sell to the users some piece of software that can correct distortion of images that are shot with their imaging products.
Optical Design literature
It is virtually impossible to search all the books that were published about lens design and their metrics during 150 years...
Near the end of the Preface of his book "Lens Design" (Fourth edition, 2006), Milton Laikin write the formula that he uses all along the chapters to define the distortion of about 150 different lenses: << Distortion is defined as D = (Yc-Yg) / Yg where Yc is the actual image height at full field and Yg is the corresponding paraxial image height. For a focal systems, D =( (tan Theta' /tan Theta) - m) / m whereTheta' is the emerging angle at full field, and m is the paraxial magnification (Kingslake1965).>> This seems equivalent to the SMIA adopted definition!
ISO 9039-2008
Foreword: the ISO 9039 Standard is totally ignoring the movement of the Entrance Pupil (EP) and this may be a problem in certain circumstances especially for photograph with very small object distance since the EP movement often induces strong distortion (bulging). More importantly, when the Standard requires that << the axis of rotation is perpendicular to the plane formed by the image height axis (and the optical axis of the collimator) and passes approximately through the midlle of the entrance pupil of the optical system to be tested.>> That implies that the Entrance Pupil is assumed to be still and this is questionable.
(Absolute) Distortion Va is defined as the measure of the deviation of the extra-axial image points from the ideal image points in a given plane lying parallel to the reference plane of the system.
The relative distortion Vr is the distance in the radial direction between the observed image point and the ideal image point, expressed as a percentage of the ideal image height h' 0.
If we assume that photography is about shooting image of an object with a finite image distance for a finite object distance, the reference quantity is the lateral magnification m and Va=h'-h m and thus Vm =100{(h' / h) -m} / m
Where the image height h' is the distance between an image point and the axis of rotational symmetry of the (optical) test specimen, expressed in miltimetres.
When referring to the maximum of distortion that occurs on an image recorded by an optical system, this definition of "relative distortion" by the International Standard Organization may then be equivalent to the SMIA TV distortion definition for instance. The occurence of mixed type of dustortion in a given lens defeatsany similarity however.
In an Annex B (informative) the ISO 9039 STD define the Picture-height distortion value as follows:
The PHD value is positive if the corner of the image format boundary is shifted away from the centre of the format (pincushion distortion) and is negative if it is shifted towards the centre (barrel distortion). The quoted PHD value is the mean value of all four corners. Picture-height distortion can be measured directly using a rectangular line-object, with dimensions equal to the intended lens format, or can be calculated from appropriate values of the relative distortion Vr using the relationship:
where Vr(H/2) is the relative distortion for an image height equal to half the height, H, of the image format and Vr(R) is the relative distortion for an image height, R, equal to half the image format diagonal.
Influence of object (e.g. checker chart) distance
The distortion depends not only on the height but also on the focus distance that the user sets on the lens (or on the camera). The distance of the object has a weak influence when it's near infinity but it is primordial when the distance of the object becomes small or very small. The reason is the movement of the entrance pupil whith the angle of the light that has neglectible effect when the distance is large. We have illustrated this phenomenon with an experiment involving two plumb lines. When they measure the distortion of camera+lens combo in order to build an image correction module, DXO recommand to take care of this fact and take partially this into account. But the focus distance is not necessarily the distance of the principal object of the scene (and subject to distortion correction). Unfortunately this is the only information that is available when only automatically reading the EXIF. The focus distance is however generally a good approximation of the object distance... but why do we ignore how DXO make the measurement? (do they use test charts of different size when they change the distance of these test charts? how many different steps?). Then why giving only a single value on the DXOMark site??
It's a pity that DXO don't apply this when they issue distortion data on their DXOMark.com site (see table above). As only one single information is given one cannot know the distance that is taken into account!
It's also a pity that none of the other specify the distance that was used. Though it's quite easy to guess the distance that Photozone used as they write the size of the sole target that they used: (1.2 x 0.8 m). BTW when Imatest is used, this also means that because neither a specific target dimension is specified nor is the distance which thus varries with the focal length and the consequence is that none of those that use the Imatest system make the distortion measurement at the same distance and therefore they shall all get a different distortion value!
What a mess!