AU2005203031A1 - Optical transfer function measurement system - Google Patents

Description

S&F Ref: 727382

AUSTRALIA

PATENTS ACT 1990 COMPLETE SPECIFICATION ,FOR A STANDARD PATENT Cc, mc- 0t' m"- Name and Address of Applicant Actual Inventor(s): Address for Service: Invention Title: Canon Kabushiki Kaisha, of 30-2, Shimomaruko 3-chome, Ohta-ku, Tokyo, 146, Japan Matthew Amison, Kieran Gerard Larkin, Stephen James Hardy Spruson Ferguson St Martins Tower Level 31 Market Street Sydney NSW 2000 (CCN 3710000177) Optical transfer function measurement system The following statement is a full description of this invention, including the best method of performing it known to me/us:- 5845c -1- OPTICAL TRANSFER FUNCTION MEASUREMENT SYSTEM Field of the Invention The present invention relates' generally to the measurement of performance characteristics of an optical imaging system and, in particular, to the measurement of the optical transfer function of optical imaging systems.

Background When it comes to image quality of an optical imaging system, the lens system, or simply lens, stands as the first, and possibly most important, link in the optical chain.

Without a sharp lens it is impossible to acquire a sharp image. However, in order to compare the sharpness of lenses an objective scientific test is needed which can be equally applied to all lenses. Sometimes the lens forms an integral part of the camera, in which case the lens system includes the lens and the imaging sensor.

The measure generally used for quantifying the imaging performance of a lens is known as the optical transfer function (OTF). The OTF consists of two components. The first component, known as the modulation transfer function (MTF), specifies how much power at a given spatial frequency is transferred through the lens, hence a measure of the contrast of the lens. The second component of the OTF is known as the phase transfer function (PTF) and specifies what spatial distortion is present for a given spatial frequency, hence a measure of the sharpness of the lens.

The OTF is generally considered to be one of the most informative measures of resolution quality in an optical system (such as a lens). Unfortunately the accurate measurement of optical system OTF is relatively difficult, except under carefully controlled laboratory conditions. A common approach to OTF measurement is to use an object with a so-called knife edge transmission function. The transmission is a binary 727382 1 -2o function, either clear or opaque to light. The object is illuminated from behind and an image of the edge is projected by the lens under test. The image intensity profile is then measured by a scanning light sensor, or light sensor array. It can be shown that the measured light intensity is related to the OTF by a mathematical operation composed of a differential and a Fourier transform. By appropriate processing of the edge image an Cc estimate of the OTF can be obtained.

t This approach to OTF measurement has a number of limitations. The limitations C of that approach include that the OTF is only measured in one orientation. Also, that approach is constrained to have ever decreasing sensitivity with increasing spatial frequency because most of the spatial information is concentrated at very low frequencies, and it cannot be tuned to frequencies of particular interest.

The manner in which a lens's OTF varies with defocus can also reveal much about the lens. Therefore to obtain useful information about a lens's resolution performance it is usually necessary to measure the OTF at several spatial locations, at several spatial frequencies, at several orientations, and at a several defocus positions.

Such a sequence of operations can often require a large number of individual measurements.

Summary It is an object of the present invention to substantially overcome, or at least ameliorate, one or more disadvantages of existing arrangements.

According to a first aspect of the present invention, there is provided a method of determining an Optical Transfer Function (OTF) of a lens system, the method comprising the steps of: providing a test chart comprising a test pattern, said test pattern comprising a plurality of sinusoidal patterns having a plurality of predetermined discrete spatial 727382 1 -3-

O

O frequencies and a plurality of predetermined orientations, wherein the amplitude of each of said sinusoidal patterns is independently adjustable in the production of said test chart; N imaging said test chart with a device comprising said lens system to produce a captured test pattern; and S 5 comparing at least one characteristic of the captured test pattern with a Scorresponding characteristic of the test pattern of said test chart to determine the Optical STransfer Function (OTF) of the lens system.

According to a second aspect of the present invention, there is provided an apparatus for determining an Optical Transfer Function (OTF) of a lens system, the apparatus comprising: a test chart comprising a test pattern, said test pattern comprising a plurality of sinusoidal patterns having a plurality of predetermined discrete spatial frequencies and a plurality of predetermined orientations, wherein the amplitude of each of said sinusoidal patterns is independently adjustable in the production of said test chart; an image sensor associated with said lens system for imaging said test chart to produce a captured test pattern; and means for comparing at least one characteristic of the captured test pattern with a corresponding characteristic of the test pattern of said test chart to determine the Optical Transfer Function (OTF) of the lens system.

According to another aspect of the present invention, there is provided a test chart for measuring an optical transfer function of a lens system, the test chart comprising a plurality of sinusoidal patterns having a plurality of predetermined discrete spatial frequencies and a plurality of predetermined orientations, wherein the amplitude of each of said sinusoidal patterns is independently adjustable in the production of said test chart.

727382 1 -4- According to yet another aspect of the present invention, there is provided a method of determining an Optical Transfer Function (OTF) of a lens system, the method comprising the steps of: providing a test chart reproduced from a predetermined test pattern, said test pattern having a plurality of frequencies in a frequency domain, said frequencies having more than one predetermined orientation in said frequency domain and having one or more frequency amplitudes independently adjusted of other frequencies of said plurality of frequencies; capturing the test chart with a device utilizing said lens system to produce a captured test pattern; comparing at least one characteristic of the captured test pattern with a corresponding characteristic of the predetermined test pattern to determine the Optical Transfer Function (OTF) of the lens system.

According to yet another aspect of the present invention, there is provided a test chart for measuring an optical transfer function of a lens system, the test chart being a spatial domain representation of a test pattern, the test pattern being characterised in a frequency domain by a plurality of frequencies, said frequencies having more than one predetermined orientation in said frequency domain and having at least one frequency amplitude independently adjusted of other frequencies of said plurality of frequencies, so as to produced a test chart, having more than one grey-scale in said spatial domain representation, adapted to measure the optical transfer function of a lens system.

According to yet another aspect of the present invention, there is provided a test chart for measuring an Optical transfer function of a lens system, the test chart comprising an image generated from a test pattern having a plurality of frequencies with more than one orientation in the frequency domain and having an amplitude of at least one 727382 1 O frequency independently adjusted to produce a plurality of grey-scales adapted to measure the Optical transfer function of the lens system.

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Other aspects of the invention are also disclosed.

Brief Description of the Drawings 5 One or more embodiments of the present invention will now be described with C€3 reference to the drawings, in which: Fig. 1 shows an example MTF graph; N, Fig. 2A shows a lens testing system for measuring the OTF of a given lens; Fig. 2B shows the preferred geometry for illumination and imaging the test chart of the lens testing system shown in Fig. 2A; Fig. 3 shows a schematic block diagram of the general purpose computer of the lens testing system shown in Fig. 2A; Fig. 4 shows a schematic flow diagram of a method of producing the test chart; Figs. 5 and 6 show steps and sub-steps of the method of Fig. 4 in more detail; Fig. 7A shows an example of the Fourier domain representation of an image tile used to form the test chart; Fig. 7B shows an example of the spatial domain representation of an image tile; Fig. 8 shows a schematic flow diagram of a method of measuring the OTF of a given lens; and Figs. 9 to 11 show steps and sub-steps of the method of Fig. 8 in more detail.

Detailed Description Where reference is made in any one or more of the accompanying drawings to steps and/or features, which have the same reference numerals, those steps and/or features have for the purposes of this description the same function(s) or operation(s), unless the .contrary intention appears.

727382 1 -6- As described in the "Background" section, in order to measure the complete OTF of a lens a large number of variables have to be controlled. Such an operation may be Ni complicated. To present a meaningful subset of the complete OTF data, the OTF of a lens is sometimes summarised by selecting a number of spatial frequencies and a number of orientations, and a graph is then produced as to' how the MTF at these frequencies and orientations varies as a function of distance from the centre of the image plane.

An MTF graph of this type is shown in Fig. 1 for an example lens. In the graph the MTF plots for the spatial frequencies of 10 and 30 line pairs per millimeter (lp/mm) are shown for line pairs in the sagittal (radial) and meridional (tangential) directions respectively, for open aperture and f/8.0 aperture, as a function of the diagonal distance, in mm, from the centre of the image plane. Such MTF graphs are common in data specifications for lenses that may be purchased commercially. The vertical axis represents the fraction of light that passes through the lens. An ideal lens would transmit 100% of the light, which is 1 on the scale. But, no lens is perfect, and therefore there are losses. The solid lines 10, 12, 16 and 18 represent sagittal measurements, while the dotted lines 11, 13, 17 and 19 represent meridional measurements. The dark lines 16, 17, 18 and 19 represent open aperture and the light lines 10, 11, 12 and 13 represent aperture. The thin lines 12, 13, 18 and 19 represent 10 lp/mm and the thick lines 10, 11, 16 and 17 represent 30 lp/mm.

Fig. 2A shows a lens testing system 100 for measuring the OTF of a given lens 150 at a number of different focus positions, a number of different spatial frequencies, and at a number of different positions across the image plane of the lens 150. The lens testing system 100 includes the lens to be tested 150, a digital camera 130 to which the lens 150 is mounted, a test chart 110, an illumination source 120 for illuminating the test chart 110, and a general purpose computer 140 connected to the digital camera 130. The 727382 1 -7- O system 100 further includes a printer 190 connected to the general purpose computer 140 for printing the test chart 110. Once the test chart 110 is produced, the printer 190 may be neglected from the system 100.

The digital camera 130 and the test chart 110 are positioned relative to each other such that the test chart 110 is approximately perpendicular to the optical axis of the Clens 150. The illumination source 120 is preferably two light sources which are Spositioned in such a way that the illumination across the test chart 110 is approximately N uniform.

Fig. 2B shows the preferred geometry for illumination and imaging the test chart 110 in more detail. The preferred placement of the digital camera 130 and lens 150 is behind the illumination sources 120. The light sources 120 are baffled to prevent light leaving the light sources 120 from directly entering the aperture of the lens 150.

For a given lens 150, such as the Canon EF50/1.4, a nominal magnification M of is preferably chosen (M 30). In this way, a 30mm feature on the test chart 110 will be imaged to a lmm feature in the image plane. Inversely, if a 30 (lp/mm) signal is to be measured in the image plane, then the signal is placed at a frequency of 1 lp/mm in the test chart 110.

It is generally desirable to measure the OTF over the full sensor size of the digital camera 130. In the preferred embodiment the digital camera 130 used is a modified sensor package from a Canon EOS 1Ds Mark II digital camera, which has a sensor 36mm wide by 24mm high, and a pixel resolution of 4992 x 3328, leading to a pixel pitch in the image plane of 7.2 microns. The sensor package has been modified to remove the low pass filter and colour filter array. It is assumed the camera sensor has been calibrated according to the ISO-14524:1999(E) standard, which specifies the optoelectronic conversion function (OECF) of the camera 130. The OECF specifies the 727382 1 -8- O correspondence between digital counts values on the camera sensor and linear input light.

The test chart 110 is large enough to fill the frame of the sensor of the camera 130 when imaged through the lens 150 under test while still being within the focus range of the lens 150.

5 For the exemplary Canon EF50/1.4 lens, at 30x magnification, the test chart 110 Shas dimensions 1080mm x 720mm, which is around AO size. The image plane of the (Ni camera 130 is situated approximately parallel to the test chart 110 at a distance 1550mm N, from the chart. In this configuration, the chart scale is 30 times the scale of the image of the chart in the image plane. Thus, if a spatial frequency of 10 lp/mm in the image plane is to be measured, a spatial frequency of around 0.33 lp/mm must be present in the test chart 110. With a sensor pixel pitch of 7.2 microns, this spatial frequency corresponds to around 14 pixels per period on the sensor.

In measuring the OTF of the given lens 150, two separate processes have to be performed. The first process is for producing the test chart, whereas the second process is for using the test chart 110 to measure the OTF of the given lens 150.

The general purpose computer 140 (Fig. 2A) controls generation and printing of the test chart 110. The general purpose computer 140 also controls the acquisition of images with the digital camera 130, including controlling the exposure of the images captured and the aperture and focus of the lens 150. Finally, the general purpose computer 140 performs the processing necessary to calculate the OTF of the lens from the acquired images. The general purpose computer 140 is. controlled through software, such as an application program, to perform the above mentioned processes. The software is loaded into the computer 140 from a computer readable medium, and then executed by the computer 140. A computer readable medium having such software or computer program recorded on it is a computer program product.

727382 1 -9- O Fig. 3 shows a schematic block diagram of the general purpose computer 140.

The computer 140 is formed by a computer module201, input devices such as a C keyboard 202 and mouse 203, and output devices including a video display 214. The computer module 201 typically includes at least one processor unit 205, and a memory unit 206. The module 201 also includes an number of input/output interfaces Sincluding a video interface 207 that couples to the video display 214, an I/O interface 213 for the keyboard 202 and mouse 203, and an interface 208 for controlling the camera 130 ,i and the printer 190. A storage device 209 is provided and typically includes a hard disk ,drive 210 and a floppy disk drive 211. A CD-ROM drive 212 is typically provided as a non-volatile source of data. The components 205 to 213 of the computer module 201, typically communicate via an interconnected bus 204 and in a manner which results in a conventional mode of operation of the computer system 200 known to those in the relevant art.

Typically, the application program is resident on the hard disk drive 210 and read and controlled in its execution by the processor 205. Intermediate storage of the program and any data may be accomplished using the memory 206, possibly in concert with the hard disk drive 210. In some instances, the application program may be supplied to the user encoded on a CD-ROM or floppy disk and read via the corresponding drive 212 or 211, or alternatively may be read by the user from a network (not illustrated). Still further, the software can also be loaded into the computer 140 from other computer readable media. The term "computer readable medium" as used herein refers to any storage or transmission medium that participates in providing instructions and/or data to the computer 140 for execution and/or processing. Examples of storage media include floppy disks, magnetic tape, CD-ROM, a hard disk drive, a ROM or integrated circuit, a magneto-optical disk, or a computer readable card such as a PCMCIA card and the like, 727382 1 O whether or not such devices are internal or external of the computer module 201.

Examples of transmission media include radio or infra-red transmission channels as well r, as a network connection to another computer or networked device, and the Internet or Intranets including e-mail transmissions and information recorded on Websites and the (cf 5 like.

The process of producing the test chart 110 to be imaged is first described with reference to Fig. 4 where a schematic flow diagram of a method 300 is shown. As stated above, the method 300 is effected by software executing on the computer 140. The method 300 starts in step 305 where the frequencies, orientations and positions in the image plane at which the OTF is to be measured are received as input from a user. The processor 205 then in step 310 uses the parameters received in step 305 to generate a digital version of the OTF measurement chart 110. Step 310 is described in more detail below with reference to Fig. 5. The digital version may be stored in a digital image file on the storage device 209.

In the preferred embodiment, the chart 110 is generated as a 300dpi greyscale TIF file format with 8 bits per pixel of colour resolution. The TIF file has dimensions 12,756 x 8,504 pixels and has an associated International Color Consortium (ICC) profile specifying that the grey values in the chart 110 correspond to linear intensity measurements.

The printer 190 is then colour calibrated in step 320, thereby producing a colour profile for the printer 190. The printer 190 may be any commercial grade large format inkjet printer, such as the CanonTM BJ W8200PG. The colour profile is then used by the computer 140 in step 330 to print an accurate greyscale test chart 110 on the calibrated printer 190. In particular, the TIF file version of the chart 110 is printed at 300dpi using greyscale printing through software that implements ICC colour management, such as 727382 1 -11o Adobe Systems Photoshop®. To ensure linear greyscale reproduction of the chart 110, an ICC profile for the printer is generated. This may be done with well known commercial products such as ProfileMakerPro by Gretag Macbeth. This ICC profile is selected for the output device ICC profile with a relative colorimetric rendering intent.

Finally, the method 300 ends in step 340 where the printed chart 110 is measured Cc to determine what the modulation and phase of each frequency and orientation pair in In each region of the chart 110 is. Step 340 is described in more detail below.

,IC Before describing step 310 where the digital version of the OTF measurement chart 110 is generated from the parameters (frequencies, orientations and positions in the image plane at which the OTF is to be measured) received in step 305, the preferred parameters are first described. In order to produce OTF information such that an MTF graph of the type shown in Fig. 1 can be produced from the output of the lens testing system 100 the positions in the image plane at which the OTF is to be measured is preferably specified as being along diagonals of the image plane, which is at an angle 33.7' to the horizontal for the example image sensor of the digital camera 130. This provides the greatest extent from the centre of the image plane. Also, the positions are specified to be in 2mm steps from -20mm to 20mm in the image plane. Hence, the positions extend from the centre and approximately to the comers of the sensor in the image plane.

Again, in order to produce OTF information such that MTF graphs of the type shown in Fig. 1 can be produced the spatial frequencies are preferably specified to be 6 lp/mm, 12 lp/mm, 24 lp/mm, 36 lp/mm, and 48 lp/mm. As is also typical, the orientations are preferably specified to be in the sagittal and meridional directions.

As there are two diagonals, one from the bottom left to the top right of the image plane and one from top left to bottom right of the image plane, those two diagonals 727382 1 -12correspond to two regions, denoted as R u respectively where j enumerate the region number, which ranges from 1 to NR =2 in the present case. In the case where the C1 diagonals are not at 450 to the horizontal of the image plane, and where the sagittal and meridional directions are chosen, each region R u will have a different set of orientations. Regions R u are thus areas of the image plane where the same set of spatial frequencies and orientations are to be measured. Within region R u each frequency and i) Sorientation pair to be measured is denoted afj)), where i ranges from 1 to the number Nj) of frequency and orientation pairs for that region R u From the preferred spatial frequencies and orientations stated above, the number Nu) is 10. Also, within region R u the positions in the image plane at which the OTF is to be measured are denoted (x where k ranges from 1 to N j the number of positions to be measured for region R u From the preferred positions stated above, the number N~ j is 21.

As described above, in the preferred embodiment there are two regions covering the diagonals of the test chart. In the centre of the test chart, these diagonals overlap. In the preferred embodiment, the region R' is considered to lie above the region R( 2 That is, the pattern placed on the test chart in the centre of the chart is taken from region R This is acceptable as at the centre of a lens, the meridional and sagittal components are both radial, so the OTF can be accurately estimated from either of the sets of frequencies in the two regions. In an alternate embodiment, a further region may be introduced that contains all the frequencies present in both R and R 2 The preferred frequency and orientation pairs (F u ,a~J for each region RU is given in Table 1: 727382 1 -13- Region R"'I Region R" 2

I

(FIl) 6lp 33.70) 2) 6lp mm,al 2 =-33.70) (N 121p/mm, a 1 33.70) (F 2) 12/p/mm, a( 2 -33.70) 241p/mm,a(' 33.70) (F(2 241p/mm, -33.70) 36lp/mm,a') 33.70) (F 2) =361p/mm, a( 2 -33.70) (Fs") 481p/mm, 33.70) (2 =481p/mm, a 2 33.70) 6lp/mm,a

I

123.70) (F62) =6lp/mm,a 2 56.30) 12lpmm, 123.70) (F2) 121p/mm, a 2 56.30) (Fs(I) =24lp/mm, 123.70) 24lp/mm, a 2 56.30) (F(E 361p mm, a9 123.70) 361p/mm a 2 56.30) 48p mm, 123.70) (F1 481p/mm, a 1 2 56.30) Table 1 Preferred frequency and orientation pairs The test chart 110 which is used in the lens test system 100 (Fig. 2B) for measuring the OTF of the given lens 150 contains combinations of sinusoidal patterns at the specified frequency and orientation pairs aJ)) which are distributed over regions of the chart 110 which corresponds to the regions R( j of the image plane of the lens 150 as defined above. Hence, the sinusoidal patterns consist of discrete spatial frequencies F,.

j The scale of the chart 110 is related to the scale of the image plane by the magnification M specified within of the lens testing system 100.

To measure the OTF accurately and to allow some tolerance in the spatial configuration of the camera 130 relative to the test chart 110, the regions R j have a spatial extent. Preferably the spatial extent of each region R' j is at least 5 periods of the 797319 1 -14lowest spatial frequency F,.j present in the region R u Accordingly, each region R j in the preferred embodiment is extended 3.3mm in the image plane away from the diagonal. In the plane of the test chart 100 at 30x magnification (M=30) this extension corresponds to a thickness of the region of around 200mm.

Having stated the preferred parameters received in step 305 and the form of the test chart 110, step 310 where the digital version of the OTF measurement chart 110 is Sgenerated from the parameters is now described in more detail with reference to Fig. where a schematic flow diagram of step 310 is shown.

Step 310 starts in sub-step 410 where the next region R is selected. In substep 420 an image tile is then generated that has image content with a frequency spectrum that will be substantially congruent with the spatial frequency and orientation pairs Ij)) required for that region R' 1 when imaged by the camera 130 in the lens testing system 100. An image tile with periodic content is generated in a manner described in more detail below with reference to Fig. 6.

In sub-step 430 that follows this image tile for the present region R j is replicated across the region R( That is, a pixel value from the image tile is assigned to corresponding pixels throughout the region R j of the digital version of the OTF measurement chart 110. If a pixel in the digital version is at position then it is assigned the value in the image tile at pixel location (X mod Tx, Y mod Ty) where Tx and Ty are the image tile width and height respectively.

In sub-step 440 the processor 205 determines whether more regions R j remain for processing. In the case where more regions R( remain, processing returns to substep 410 from where the next region R j is incorporated into the digital version of the measurement chart 110. Alternatively step 310 ends.

727382 1 Fig. 6 shows a schematic flow diagram of sub-step 420 where the image tile is generated in more detail. Each image tile is specified by the spatial frequency and N, orientation pairs required for that region R u To determine the size of the tile, hence the tile width Tx and height Ty, and the frequencies that should be included in the image tile, it is necessary to know the approximate magnification M between the image plane and the plane of the test chart 110. For the illustrative example given above for the 50mm lens, the magnification M between the plane of the test chart 110 and the image plane is 30. The tile size is related to the lowest spatial frequency F,. present in the region R' which is 6 p/mm in the image plane for the preferred embodiment. That spatial frequency F,.j in the image plane relates to a frequency of 0.2 lp/mm on the plane of the test chart 110. A horizontal frequency of 0.2 lp/mm corresponds to around pixels per horizontal line pair on the test chart 110 at 300 dpi. The orientation of the sagittal and meridional line pairs implies a horizontal distance of around 50 pixels per line pair. Thus, to have a periodic tile, the tile must have a horizontal size close to a multiple of 50 pixels otherwise the 6 lp/mm sinusoid could not be accurately represented. The tile size chosen in the preferred embodiment is 200 pixels.

Accordingly, an empty tile of width Tx and height Ty is created in sub-step 510.

This tile consists of a raster array of complex values which are initially considered to be in the Fourier domain. The coordinate positions of the pixels in the image tile also relate to spatial frequencies on the test chart 110. If the pixels in the tile are laid on a coordinate grid with the upper left of the tile defining the origin and the lower right of the tile defining coordinate (Tx 1, Ty then a pixel at position 1Y) would correspond to a spatial frequency on the test chart 110 of: 727382 1 -16xTx 2 (1) where F, and F, are the horizontal and vertical spatial frequency components respectively, measured in lp/mm on the test chart 110, and D is the printer resolution measured in dots per mm.

In sub-step 520, the (next) of the (remaining) spatial frequency and orientation pairs (F) that are to be placed in the image tile is selected. The approximate spatial frequencies to be placed into the chart 110 are given by: Fx'= F.

j cos a j

/M,

(2) Fi j sin a /M For example, the first of the preferred spatial frequency and orientation pairs is (F =61p/mm, 33.70). Using Equation the approximate spatial frequencies to be placed into the chart 110 are 0.08321p/mm and Fy'= 0.0555 Ip/mm. However, these frequencies F x and Fy' cannot be exactly represented in the image tile, due to the quantisation of the frequencies to pixel positions in the Fourier frequency domain. In sub-step 530 the frequencies and Fy' are quantised to lie on pixel positions in the Fourier frequency domain representation of the image tile. The quantised positions are given by: Q[r J <Tx Qx x+ 0.

5 S(3) Q [i D s+ 0.5 1 wherein represents the ceiling function.

727382 1 -17- In sub-step 540 peaks are placed in the tile in the Fourier domain at pixel position Q and at the Hermitian conjugate position by placing a unit Smodulus and zero phase complex value in each of those two positions. Other values of the modulus and phase may be used, though if a non-zero phase is used then the conjugate of the complex value with that phase must be placed in the Hermitian conjugate position Qx,-Q to ensure that the inverse Fourier transform of the tile remains real.

0The processor 205 then determines in sub-step 550 whether any more spatial frequency and orientation pairs (F u aj)) remain for processing. In the case where more spatial frequency and orientation pairs (Fi),a a) remain, processing returns to sub-step 520 from where peaks corresponding to the next spatial frequency and orientation pair are placed on the tile in the Fourier domain.

Sub-steps 520 to 550 are repeated until peaks corresponding to each spatial frequency and orientation pair are placed in the Fourier domain. The quantised x and y spatial frequencies of the ith spatial frequency and orientation pair are denoted (Qx) Qy). Fig. 7A shows an example of the Fourier domain representation of the tile. In particular, the magnitude of the Fourier domain representation is shown. The configuration of the peaks in the sagittal and meridional directions is apparent.

Sub-step 560 then follows where the tile is transformed to the spatial domain using the discrete inverse Fourier transform. This step transforms the tile from the frequency domain representation that it was generated in to a spatial domain representation. It is the spatial domain representation that is ultimately used to create the digital version of the OTF measurement chart 110. In the final sub-step of step 420, substep 570, the range of values in the spatial domain representation of the tile are rescaled to 727382 1 -18a range between 0 and 255 which is appropriate for storage in a digital TIFF image file.

This completes the tile generation sub-step 420.

C1 Due to the periodic nature of the discrete Fourier transform, the tile itself is periodic and can be replicated across the associated region R j of the test chart 110 without introducing spurious frequency artefacts.

SFig. 7B shows an example of the spatial domain representation of the tile. In the representation image values with a value of 255 is represented as white, while image values with a value of 0 is represented as black. Also, for purposes of illustration halftoning has been applied to those values. The actual test chart is printed in step 330 using greyscale printing.

The characteristics of the test chart 110 after it has been printed do not match the characteristics of the digital version of the chart exactly. This is because the printing process is not perfect. In particular, the printer 190 only has a limited number of inks which are printed in a half tone pattern to give the appearance of shades of grey when viewed from normal viewing distance. This half-toning process means that the amplitudes and phases of the frequency peaks that have been embedded in the tile are not exactly reproduced on the printed test chart 110. To ensure accurate OTF measurements, it is important to compensate for this effect. Furthermore, the non-zero reflectivity of the darkest patch printable by the printer 190 means that the luminance of the black achievable by the printer 190 is generally only one hundredth of the luminance of a white sheet of paper, as opposed to the effectively zero luminance achievable in the digital version of the test chart.

To compensate for these effects, the printed test chart 110 is calibrated. A brief description of this calibration process is that each region R j of the printed test chart 110 is imaged using a high-quality macro lens at lx magnification. The amplitudes and 727382 1 -19phases of the frequencies present in the imaged region, denoted (G j 8 j and the zero Sfrequency offset for the imaged region (which is approximately the DC value of the tile that covers the region), denoted Go(j), are stored for later use. The use of the high quality _macro lens assures that the frequencies when imaged by the macro are in a region of the lens where the OTF is essentially real and unit magnitude, and where the attenuation I effects of the camera sensor package are not significant. In the preferred embodiment this lens is a CanonTM MP-E65mm f/2.8 1-5x Macro lens. A detailed description of this calibration process is given below.

The allowed tolerances in the physical imaging geometry of the test chart 110 relative to the camera 130 that is illustrated in Fig. 2B are now described in more detail.

The camera 130 is positioned relative to the test chart 110 such that the optical axis of the lens 150 intersects the centre of the test chart 110 within 3% of the chart width. The distance of the image plane of the camera 130 to the test chart 110 is such that the preselected magnification M, which is 30x in the illustrative configuration, is achieved to within Also, the camera 130 is rotated around the optical axis of the lens 150 such that a horizontal line on the sensor matches a horizontal line on the test chart 110 to within 20. Yet further, the camera 130 is positioned such that its pan and tilt relative to the test chart 110 are within 1 All of these parameters are easily achievable using industry standard camera mounts.

In the preferred embodiment the camera 130 is connected to the computer 140 by a computer interface cable, such as a FirewireTM cable, over which the computer 140 controls the exposure settings of the camera 130 and the aperture and focus settings of the lens 150. If the camera 130 used in the lens test system 100 does not allow computer controlled focus position setting for its attached lenses, the camera 130 may be mounted on a mechanical positioning stage so that the camera 130 may be moved towards and 727382 1 O away from the test chart 110 to adjust the focus position, either manually or under computer control.

N ~After the test chart 110 and the camera 130 have been mounted in an appropriate imaging configuration the OTF of a lens may be measured. Fig. 8 shows a schematic flow diagram of a method 600 of measuring the OTF of the given lens 150. Prior to measuring the OTF of the lens 150 the focus positions at which the OTF of the lens 150 is t to be measured are chosen. The OTF of any lens depends strongly on its focus position, N so ensuring that the plane of best focus has been achieved is important in measuring the OTF of the lens 150.

Often cameras have automatic focus measurements, though sometimes they do not achieve the plane of best focus consistently and reliably. To that end, in the preferred embodiment a number of OTF measurements for the lens are made at a number of different focus positions. The approximate best focus position may be determined using the auto-focus mechanism of the camera 130. The lens may then be drivefi to just short of the approximate best focus position and a number of images may be taken at a sequence of focus positions until after the approximate best focus position. There is a compromise that has to be made between the number of different focus measurements that are taken, and hence the accuracy with which the best focus plane is determined, and the time the measurement of the lens OTF takes. In the preferred embodiment 5 images at equally spaced intervals around the approximate best focus given by the camera auto-focus system are taken. This is considered an appropriate balance between determining the best focus position and the time it takes to measure the OTF of the lens 150.

It also should be noted that the best focus position varies across the image plane.

The locus of the best focus position describes a two dimensional surface through which 727382 1 -21o the image plane slices. If a dense set of focus positions are measured, this surface of best focus, the Petzval surface, may be determined.

N The method 600 starts in step 605 where the lens 150 to be measured is connected to the camera 130 through its standard mount, such as a bayonet mount. In step 610 the focus position of the lens 150 is set to a first position. The camera 130 is ¢€3 then controlled in step 620 to capture an image of the test chart 110. When capturing the image the aperture of the lens 150 is set to wide open, which for the example 50mm lens is f/1.4. Also, the exposure of the camera 130 is set such that the maximum value from the white part of the test chart 110 is approximately 2500 counts. This is to ensure that the image signal is in a region of good signal to noise ratio and that the image sensor of the camera 130 is operating in a range where its output may be accurately linearized using the OECF. The image is preferably captured in a RAW file format, such as the Canon RAW file format which returns raw digital sensor counts in a CR2 file. It will be understood by one skilled in the art that the OTF of a lens may be measured at any aperture.

In step 630 the RAW file format image file containing the image of the test chart 110 is transferred to the computer 140. The processor 205 of the computer 140 then in step 640 converts the raw sensor counts which are extracted from the RAW file format image file to linear light values. This is done by utilising the results of the measurement of the OECF of the camera according to ISO 14524:1999(E) standard. Each pixel in the RAW image is converted according to the OECF to produce an image of the test chart 110 which is substantially proportional to the intensity of light impinging on the image sensor of the camera 130.

727382 1 -22o In step 660 the OTF of the lens 150 for the given focus position is determined from the corrected and white balanced image of the test chart in the manner described in N, more detail below with reference to Fig. 9.

In step 670 it is then determined whether all focus positions have been imaged.

C 5 If it is determined that focus positions remain to be imaged then processing returns to step 610 from where a next focus position is set, imaged, and an OTF determined for that t focus position.

C If it is determined in step 670 that all the focus positions have been processed then the method 600 terminates in step 680 where the OTF values determined in step 660 for each focus position are output for further processing and examination by the user.

Generally the OTF values will be examined at the centre of the image for each focus position, and the focus position with the highest MTF will be considered the best focus position. All of the OTF values calculated in step 660 for this best position will then be presented to the user as the OTF for the lens 150 at best focus.

Step 660 in which the OTF of the lens 150 is determined for a given focus position is now described in more detail with respect to Fig. 9 where a schematic flow diagram of step 660 is shown. The input to step 660 is the linearized and white-balanced image of the test chart 110. Using this image, in sub-step 720 a next region R( j for which the OTF is to be measured is identified and selected for processing. Then, in substep 730 a tile which covers approximately the same area as the tile embedded in the printed test chart 110 in step 420 and corresponding to position (x j yJ)) of the image plane for the present region R j is extracted from the linearized and white-balanced image. For the illustrative example of a 30x magnification, the tile size extracted is 78 pixels high by 78 pixels wide.

727382 1 -23o If the camera has been positioned relative to the test chart 110 within the tolerances given above, then the tile extracted from the image will contain a collection of N, sinusoids of approximately the spatial frequencies F2j) specified when the test chart 110 was designed.

Determining the amplitude and phase of these sinusoids in the extracted tile determines how much of the amplitude present in the printed chart survives Stransmission through the lens, and how much the phase li) of the sinusoid was shifted by transmission through the lens 110, and thereby what the OTF of the lens is at that frequency and orientation. Accordingly, in sub-step 740, the frequency, amplitude and phase of the sinusoids present in the tile are determined in a manner described in more detail below with reference to Fig. The frequency, amplitude and phase of the sinusoids present in the tile determined in sub-step 740 are then adjusted in sub-step 750 to take into account the relative strengths G j and phases fl/' of the sinusoids that were present in the printed version of the test chart 110, the OTF of the sensor of the camera 130 and the geometry of the lens testing system 100. Sub-step 750 is described in more detail below with reference to Fig. 11.

In sub-step 760 the adjusted amplitudes and phases for each sinusoid present in the tile are stored for later presentation to the user in step 680 (Fig. It is next determined in sub-step 770 whether all the positions in the present region R(i) have been processed. In the case where positions remain the processing returns to sub-step 730 from where a next tile is extracted and processed.

After all the positions for the present region have been processed, it is determined in sub-step 780 whether all the region R u have been processed. In the case 727382 1 -24- 2 where a region R u remains processing returns to sub-step 720 from where the next region R u is processed. Otherwise step 660 terminates.

C Step 740 where the frequency, amplitude and phase of the sinusoids present in the tile are determined is now described in more detail with respect to Fig. 10 where a schematic flow diagram of step 740 is shown. Step 740 receives as input the tile extracted in step 730 (Fig. 9) from the image of the test chart 110.

SIn the preferred embodiment, an iterative non-linear fitting method is used to determine the frequency, amplitude and phase of the sinusoids present in the tile. This minimisation process fits a function of the form:

N(

I(x,y) A) A sia,Qx +axQy) +(aQx j a Qy (4) k=1 to the image data, where N) is the number of quantised spatial frequency and orientation pairs (Qx^JQy that were embedded in the tile when the test chart 110 was produced. The iterative least squares algorithm minimises the squared residual error between the image data and this functional form by varying A k, A j k 1 N :k a ay, and a In the expression of Equation the coefficients a a, and a, represent a possible affine transform between the image plane and the plane of the test chart 110. This compensates for local changes of magnification and small errors in the setup of the geometry of the lens testing system 100.

After minimisation, the parameters Ak k e NF and (p k e N) represent the amplitudes and phases of the sinusoids present in the tile, respectively.

Non-linear minimisation requires initial conditions for the variables which are being fit. These initial conditions are set in sub-step 820 as follows: A? Mean of tile values; 727382 1 A§ k e NF) Standard deviation of tile values divided by N;

(N

a,,ayy: 2;r/Tx; and axy ay x 0.

5 The minimisation is performed in step sub-830. In the preferred embodiment a non-linear least squares minimisation scheme, known as Levenberg-Marquardt Sminimisation, is used. Such methods are well known in the art. In sub-step 840 which follows the relative residual error E from the fitting process is determined. If the pixel values in the tile are given by T(x, then the relative residual error E is given by: S(T(x, y) I(x, y)) 2 E x,y T(x, )2 CT(x, Y) 2 x,y The quantum of the residual error E is a guide as to whether there has been any problem in the OTF measurement for this tile. A residual error E value of more that 0.04 suggests that there has been a problem in the measurement and the user should examine the setup of the camera 130 to ensure it is within the tolerances given above, and the captured image should be examined to ensure that it is free of defects, such as those caused by dust on the sensor.

Step 740 ends in sub-step 850 where the amplitudes A A k e Nj and phases po) k e and affine fit co-efficients ay, a x and a, of the sinusoids present in the tile are output for use in step 750 (Fig. 9).

Step 750 (Fig. 9) where the amplitudes A j A and phases (Op of the sinusoids present in the tile determined in step 740 are adjusted to take into account the relative strengths and phases of the sinusoids that were present in the printed version of 727382 1 -26o the test chart 110, the OTF of the sensor of the camera 130 and the geometry of the lens test system 100 is now described in more detail with reference to Fig. 11. where a schematic flow diagram of step 750 is shown. Step 750 receives as input the values of

A

i

A

j ke N( and k e N a, ay,, and ay defining the best

C

r 5 fit affine transform from step 740, as well as the frequencies, amplitudes and phases of Sthe sinusoids in the present tile. Step 750 starts in sub-step 920 where the frequencies of the sinusoids embedded in the chart (Qxj),Qy( j are modified by the best fit affine transform output by step 740. This identifies the frequencies that were measured in the image plane of the lens 150. The sinusoids identified in the tile are of the form: sin(aQx j ayQyl (aQx j ayyy j )y ok thus the measured x and y spatial frequencies are at j) (aQxj) a QyIj)) 2,rA (6) (ay Qx j ayyQy j 2nA where A is the pixel spacing on the image sensor of the camera 130. Given that the magnification M may be up to 5% away from the target magnification, and that lenses often exhibit substantial local spatial deformations, then the frequencies present in the captured image may be more than 5% away from those chosen at the time the test chart 110 was designed and constructed. While for many applications the 5% change in frequency may be unimportant, sub-step 920 calculates this information so that it may be supplied to the user.

In sub-step 930 the amplitudes Aj, A and phase <p of the sinusoids detected in the tile are corrected for systematic effects that are introduced by the sampling by the sensor in the camera 130. A particularly important effect introduced by the sensor 727382 1 -27o is caused by the fact that the light sensitive area of each pixel does not cover the entire area of the pixel. This under-sampling of the image plane leads to unwanted Moire effects in images. Generally, these Moire patterns are mitigated in digital still cameras by placing a spatial low-pass filter in between the lens 150 and the surface of the image sensor of the camera 130. As stated before, the sensor package of the camera 130 used for imaging the test chart 110 has preferably been modified to remove this low pass filter, t as the filter reduces the sensitivity of the sensor to the spatial frequencies that are to be N measured. However, in this case, the effect of the under-sampling of the image plane by the sensor package should be explicitly modelled and accounted for.

A simple model of the effect introduced by the fact that the light sensitive area of each pixel does not cover the entire area of the pixel is given here which is sufficient to allow accurate measurements of the OTF. The sensor sites are square with spacing A (in mm) and the active area of a pixel is assumed to be square with dimension W (in mm).

The relative amplitude of a spatial frequency (wxiJ), oy~' j (measured in lp/mm) as sampled by the spatial grid is given by: sin n-rxm W sin nwo }JW (7) )TO)XUW 7oy!D"W where also, at the limit of zero frequency, the relative amplitude is one. For a nominal value of W=4.32 microns, at 48 lp/mm in the horizontal direction, this value is approximately 0.866. In sub-step 930, the amplitudes for each frequency are adjusted by dividing the amplitudes detected at that frequency by the relative amplitude given by Equation In sub-step 940, the amplitudes A A' and phases pj) of the sinusoids detected in the tile are corrected to take into account the amplitudes G(o j GV and phases 727382 1 -28- D y fi) present in the printed test chart 110. The amplitudes Gi and phases fJ) present in the test chart 110 are determined in step 340 which is described in more detail C1 below. The MTF values for the sinusoid present in the tile are given by S GO k N (8) C4j j GFa The PTF values for the sinusoid present in the tile are given by S -Pk(: j N) (9) These MTF and PTF values are output for use in step 760.

A detailed description of the printed test chart calibration step 340 is now given.

As noted above, the printed test chart calibration is performed by using a high quality macro lens at low magnification in a configuration similar to that used in the OTF testing.

In the preferred embodiment, this lens is a CanonM MP-E65mm f/2.8 1-5x Macro lens and the lens 150 is set up in a geometry similar to that shown in Fig. 2B except that the camera 130 and lens 150 are now close to the test chart 110, approximately 50mm away.

The camera 130 and lens 150 are used to image each region R^ of the test chart 110 individually, and the OTF is determined by performing method 600 (Fig. In this calibration process, it is assumed in step 720 (Fig. 9) that there is only one region R that being the region R' that is being imaged. Also, in step 730 the whole image is used as a tile. Yet further, step 750 is not performed during the normalisation process. In step 760, the amplitudes G^ and phases fl of the frequencies present in the region, and the zero frequency offset Gi (which is approximately the DC of the tile that covers the region) for the region, are stored for later use in the compensation step 940 (Fig. 11).

The OTF determined through method 600 provides an objective scientific test with which lenses may be compared.

727382 1 -29o The foregoing describes only the preferred embodiment of the present invention, and modifications and/or changes can be made thereto without departing from the scope and spirit of the invention, the embodiment being illustrative and not restrictive. In particular, the preferred embodiment has been described in terms of a test chart 110 printed on a large format bubble jet printer. Other printing devices may be used to Cc produce the test chart 110. These include, but are not limited to, ink based printers, Selectro-photographic printing processes, photographic printing processes, and photo- CNI lithographic processes. Any device that may produce a test chart 110 with apparently multiple shades of gray at the sampling rate of the image sensor may be used to produce the test chart 110.

Furthermore, the preferred embodiment has been described in terms of a system 100 that has wide tolerances for error in terms of placement of the camera 130 in the imaging geometry. This wide tolerances are allowed due to the fact that the test chart 110 has a tiled pattern that extends over a wide spatial region, and that the analysis method is able-to determine the true relationship between the image plane and the test chart plane, and thereby return to the user the actual frequencies that were measured by the OTF measurement system 100. This property of the test chart 110 that it may be used with loose spatial tolerances in the imaging geometry due to the periodic nature of the test chart 110 is known as a "passive alignment" property. That is, the chart 110 requires no active alignment to place the OTF measuring portion of the chart in a precise position on the sensor.

In a different embodiment of the invention, these tolerances may be eliminated by using precisely machined parts to ensure that the alignment of the system is such that the test chart 110 is always imaged in the same way. In such an embodiment, the tiled 727382 1 o pattern would not be repeated over a large spatial extent and would not have the passive alignment property.

In a further variation from the preferred embodiment, the compensation steps 340, 930 and 940 may be excluded and the system may be run in a relative comparison 5 mode. In this embodiment, the system does not measure absolute OTF, however it can be used to compare the OTF of two lenses to determine which is of better quality. In that t way, if a lens is determined to have a minimum acceptable quality, any lens that has a Ci better OTF may be deemed to have acceptable quality, and any lens that has a worse OTF may be deemed to have unacceptable quality.

While the preferred embodiment of the invention has been described in terms of a lens OTF measurement system 100, it will be apparent to one skilled in the art that this technique can be used for the measurement of the OTF of other imaging devices. For instance, the OTF of a scanner may be determined by scanning an appropriately sized test chart.

Furthermore, while the detailed description above describes the measurement of the OTF a given lens 150, if the lens OTF is known, then the system can be used to quickly and accurately determine the OTF of the printer 190 that has been used to produce the chart 110.

Some digital still cameras, such as those commonly used by consumers, have fixed non-interchangeable lenses. With detailed knowledge of the sensor characteristics in such a camera, the preferred embodiment can be used to determine the OTF of the lens in situ in the camera. Furthermore, even without detailed knowledge of the sensor characteristics, the OTF of the camera as a whole including the effects of the sensor and lens and focus system may be determined. This process can form a valuable method for determining the comparative quality of a digital still camera.

727382 1 -31 The preferred embodiment of the invention as described uses a least squares fitting algorithm to determine the amplitudes and phases of the sinusoids present in the N image of the chart 110. Other analysis methods may be used to determine this information, including other parameter estimation methods such as maximum likelihood and maximum entropy methods, or other well known direct methods for estimating the amplitude and phase such as a discrete Fourier Transform.

Another quality measure for a lens is the amount of chromatic aberration it iN displays. Chromatic aberration is caused by differences in refractive index of the material that constitutes the lens as a function of the wavelength of light. These differences in refractive index lead to wavelength dependant magnification and light propagation. This means that the image formed by the lens for blue light may be different from the image formed by red light. These differences are readily apparent in poor quality lenses as they lead to colour fringing artefacts in the final image. The chromatic aberration of a lens may be measured by the preferred embodiment by modifying the light that enters the lens so that only a narrow wavelength band is imaged on the sensor and thereby evaluating the OTF of the lens as a function of wavelength. The modification may be carried out by placing a sequence of narrow band filters over the lens to change the light entering the lens, or by using narrow band illumination sources such as LEDs to change the light being reflected off the test chart 110.

As described above, in step 540 a peak is placed in the Fourier representation of a tile by placing a unit modulus and zero phase complex value in a given pixel position.

Other complex values may be placed in the Fourier representation of a tile in Hermitian conjugate pairs. In particular, for some lenses it may be advantageous to increase the modulus of the higher spatial frequency signals. Increasing the modulus effectively increases the signal present at that frequency and thereby increases the signal to noise 727382 1 -32o ratio in the measurement of that frequency. This may be advantageous as a lens generally has a lower MTF at high spatial frequencies, so increasing the input power at higher N frequencies may lead to a similar signal to noise ratio for all the sinusoidal signals measured. Furthermore, the phases of the peaks placed in the tile can also be varied from Cc 5 the zero phase described above.

In the context of this specification, the word "comprising" means "including t' principally but not necessarily solely" or "having" or "including", and not "consisting C1 only of'. Variations of the word "comprising", such as "comprise" and "comprises" have correspondingly varied meanings.

727382 1

Claims (19)

1. A method of determining an Optical Transfer Function (OTF) of a lens system, the method comprising the steps of: providing a test chart comprising a test pattern, said test pattern comprising a plurality of sinusoidal patterns having a plurality of predetermined discrete spatial frequencies and a plurality of predetermined orientations, wherein the amplitude of each N, of said sinusoidal patterns is independently adjustable in the production of said test chart; imaging said test chart with a device comprising said lens system to produce a captured test pattern; and comparing at least one characteristic of the captured test pattern with a corresponding characteristic of the test pattern of said test chart to determine the Optical Transfer Function (OTF) of the lens system.

2. The method according to claim 1 wherein said lens system comprises a lens and an image sensor.

3. The method according to claim 1 or 2 wherein said test pattern fill regions of said test chart that correspond with regions of said lens system for which said characteristics are to be measured.

4. The method according to any one of claims I to 3 wherein said comparing step includes determining at least one of the amplitude and phase of said sinusoidals. 727382 1 -34- o 5. The method according to claim 4 wherein said comparing step further comprises adjusting said amplitudes and/or phases to compensate for the effect from Z elements that are excluded from said imaging system.

6. The method according to claim 4 or 5 wherein said comparing step further Cc comprises adjusting said characteristics to compensate for the geometry of the lens V) system relative to said test chart.

7. The method according to claim 4 wherein said determining step is performed by minimisation in the spatial domain.

8. The method according to claim 4 wherein said determining step includes a discrete Fourier transform of the image data.

9. The method according to claim 4 wherein said determining step includes determining the frequencies of said measured sinusoidals, and where said determined sinusoidal frequencies are constrained to be an affine transform of the said test pattern sinusoidals.

10. An apparatus for determining an Optical Transfer Function (OTF) of a lens system, the apparatus comprising: a test chart comprising a test pattern, said test pattern comprising a plurality of sinusoidal patterns having a plurality of predetermined discrete spatial frequencies and a plurality of predetermined orientations, wherein the amplitude of each of said sinusoidal patterns is independently adjustable in the production of said test chart; 727382 1 O an image sensor associated with said lens system for imaging said test chart to produce a captured test pattern; and means for comparing at least one characteristic of the captured test pattern with a corresponding characteristic of the test pattern of said test chart to determine the Optical Transfer Function (OTF) of the lens system.

11. A test chart for measuring an optical transfer function of a lens system, N, the test chart comprising a plurality of sinusoidal patterns having a plurality of predetermined discrete spatial frequencies and a plurality of predetermined orientations, wherein the amplitude of each of said sinusoidal patterns is independently adjustable in the production of said test chart.

12. A method of determining an Optical Transfer Function (OTF) of a lens system, the method comprising the steps of: providing a test chart reproduced from a predetermined test pattern, said test pattern having a plurality of frequencies in a frequency domain, said frequencies having more than one predetermined orientation in said frequency domain and having one or more frequency amplitudes independently adjusted of other frequencies of said plurality of frequencies; capturing the test chart with a device utilizing said lens system to produce a captured test pattern; comparing at least one characteristic of the captured test pattern with a corresponding characteristic of the predetermined test pattern to determine the Optical Transfer Function (OTF) of the lens system. 727382 1 -36- O 13. The method of determining the Optical Transfer Function (OTF) of a lens system as claimed in claim 12, wherein the test pattern is positioned on said test chart at one or more locations corresponding to a spatial region of an image produced by the lens system for which the Optical Transfer Function is to be determined. S14. The method of determining the Optical Transfer Function (OTF) of a tt lens system as claimed in claim 12, wherein a plurality of said test patterns are positioned N, on said test chart to determine the Optical Transfer Function at a plurality of corresponding spatial regions of an image produced by the lens system. The method of determining the Optical Transfer Function (OTF) of a lens system as claimed in claim 12, wherein the amplitude of all of the plurality of frequencies are adjusted independently of the other frequencies.

16. The method of determining the Optical Transfer Function (OTF) of a lens system as claimed in claim 12 or 13, wherein the test chart is designed with sufficient redundancy to provide passive alignment between the captured test pattern and the predetermined test pattern.

17. The method of determining the Optical Transfer Function (OTF) of a lens system as claimed in claim 12, 13 or 15, wherein said independently adjusted frequency amplitudes provide a plurality of grey-scales in a spatial domain of the test chart. 727382 1 -37-

18. The method of determining the Optical Transfer Function (OTF) of a lens system as claimed in claim 17, wherein said grey-scales are generated by halftoning binary colours.

19. The method of determining the Optical Transfer Function (OTF) of a lens system as claimed in any one of claims 12 to 18, wherein the Optical Transfer Function (OTF) of a lens system is a Modulation Transfer Function (MTF) of the lens system.

20. A test chart for measuring an optical transfer function of a lens system, the test chart being a spatial domain representation of a test pattern, the test pattern being characterised in a frequency domain by a plurality of frequencies, said frequencies having more. than one predetermined orientation in said firequency domain and having at least one frequency amplitude independently adjusted of other frequencies of said plurality of frequencies, so as to produce a test chart, having more than one grey-scale in said spatial domain representation, adapted to measure the optical transfer function of a lens system.

21. A test chart for measuring an Optical transfer function of a lens system, the test chart comprising an image generated from a test pattern.having a plurality of frequencies with more than one orientation in the frequency domain and having an amplitude of at least one frequency independently adjusted to produce a plurality of grey- scales adapted to measure the Optical transfer function of the lens system. 727382 1 -38-

22. A method of determining an Optical Transfer Function (OTF) of a lens system, said method being substantially as described herein with reference to the accompanying drawings.

23. Apparatus for determining an Optical Transfer Function (OTF) of a lens c system, said apparatus being substantially as described herein with reference to the tt accompanying drawings. DATED this 12th Day of July 2005 CANON KABUSHIKI KAISHA Patent Attorneys for the Applicant SPRUSON&FERGUSON 727382 1