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US20020118457A1 - Wavefront coded imaging systems - Google Patents

Wavefront coded imaging systems Download PDF

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Publication number
US20020118457A1
US20020118457A1 US09/747,788 US74778800A US2002118457A1 US 20020118457 A1 US20020118457 A1 US 20020118457A1 US 74778800 A US74778800 A US 74778800A US 2002118457 A1 US2002118457 A1 US 2002118457A1
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Prior art keywords
transfer function
wavefront coding
lens
coding element
optical transfer
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Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Abandoned
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US09/747,788
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English (en)
Inventor
Edward Dowski
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Omnivision CDM Optics Inc
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Individual
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Priority to US09/747,788 priority Critical patent/US20020118457A1/en
Assigned to CDM OPTICS, INCORPORATED reassignment CDM OPTICS, INCORPORATED ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: DOWSKI, EDWARD RAYMOND JR.
Priority to PCT/US2001/044159 priority patent/WO2002052331A2/fr
Priority to EP01272457A priority patent/EP1346251A2/fr
Priority to AU2002219861A priority patent/AU2002219861A1/en
Publication of US20020118457A1 publication Critical patent/US20020118457A1/en
Assigned to REGENTS OF THE UNIVERSITY OF COLORADO, THE reassignment REGENTS OF THE UNIVERSITY OF COLORADO, THE QUITCLAIM Assignors: DOWSKI, EDWARD RAYMOND
Priority to US10/407,708 priority patent/US6940649B2/en
Priority to US11/192,572 priority patent/US7106510B2/en
Priority to US11/511,023 priority patent/US7554732B2/en
Priority to US11/511,022 priority patent/US7554731B2/en
Abandoned legal-status Critical Current

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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0025—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 for optical correction, e.g. distorsion, aberration
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/42—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect
    • G02B27/46—Systems using spatial filters
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B5/00—Optical elements other than lenses

Definitions

  • This invention relates to apparatus and methods for optical design based on wavefront coding combined with post processing of images.
  • Traditional optical design is based on the premise that the only major components of the imaging system are the optics and detector.
  • the detector can be analog (e.g. film) or a digital (e.g. CCD, CMOS etc.) detector.
  • Traditional image processing techniques performed on an image are performed after the image is formed. Examples of traditional image processing include edge sharpening and color filter array (CFA) color interpolation.
  • Traditional optics are therefore designed to form images at the detector that are sharp and clear over a range of field angles, illumination wavelengths, temperatures, and focus positions. Consequently, a trade off is made between forming good images, which requires optical designs that are larger, heavier, and contain more optical elements than are desirable, and modifying the design in order to reduce size, weight, or the number of optical elements, which results in loss of image quality.
  • Wavefront Coding systems share the task of image formation between optics and digital processing. Instead of the imaging system being primarily composed of optics and the detector, Wavefront Coding imaging systems are composed of optics, detector, and importantly, processing of the detected image.
  • the detector can in general be analog, such as film, or a digital detector. Since processing of the detected image is an integral part of the total system, the optics of Wavefront Coded imaging systems do not need to form sharp and clear images at the plane of the detector. It is only the images after processing that need to be sharp and clear.
  • Wavefront Coding in general, corrects for known or unknown amounts of “misfocus-like” aberrations. These aberrations include misfocus, spherical aberration, petzval curvature, astigmatism, and chromatic aberration. System sensitivities to environmental parameters such as temperature and pressure induced aberrations, and mechanical focus related aberrations related to fabrication error, assembly error, drift, wear, etc., are also reduced with Wavefront Coding. Optical designs based on Wavefront Coding can reduce the effects of these aberrations and result in simpler designs that produce good images.
  • Optical system designs according to the present invention are improved in that they have the characteristic that the transverse ray intercept curves are substantially straight lines.
  • the transverse ray intercept curves for wavefront coded systems need not have a near zero slope; the slope, which indicates misfocus, may be substantial, because wavefront coding allows the effects due to misfocus to be removed.
  • the transverse ray intercept curves should vary mainly in slope over wavelength, field angles, temperature, etc. but need not be exactly straight lines. Some ripple is acceptable. With wavefront coding optical surfaces and post processing, good images can be produced.
  • FIG. 1 shows a single-lens miniature imaging system according to the present invention.
  • FIG. 2 illustrates a series of transverse ray intercept curves illustrating aberrations at various wavelengths, for the system of FIG. 1 with wavefront coding removed.
  • FIG. 3 illustrates distortion curves for the system of FIG. 1 with wavefront coding removed.
  • FIG. 4 illustrates modulation transfer functions (MTF) for the system of FIG. 1, with wavefront coding removed.
  • FIG. 5 illustrates modulation transfer functions (MTF) for the system of FIG. 1, with wavefront coding, but without post processing.
  • MTF modulation transfer functions
  • FIG. 6 illustrates modulation transfer functions (MTF) for the system of FIG. 1, with wavefront coding, both before and after filtering.
  • MTF modulation transfer functions
  • FIGS. 7 a and 7 b illustrates sampled point spread functions (PSF) for the system of FIG. 1, with wavefront coding and after filtering, for two object distances.
  • PSF sampled point spread functions
  • FIG. 8 shows a low cost microscope objective according to the present invention.
  • FIG. 9 illustrates a series of transverse ray intercept curves illustrating aberrations at various wavelengths, for the system of FIG. 8 with wavefront coding removed.
  • FIG. 10 illustrates modulation transfer functions (MTF) for the system of FIG. 8, without wavefront coding; with wavefront coding; and with both wavefront coding and filtering.
  • MTF modulation transfer functions
  • FIG. 11 shows a passive athermalized IR imaging system according to the present invention.
  • FIG. 12 illustrates a series of transverse ray intercept curves illustrating aberrations at various wavelengths, for the system of FIG. 11, without wavefront coding.
  • FIG. 13 illustrates modulation transfer functions (MTF) for the system of FIG. 11, without wavefront coding.
  • FIG. 14 illustrates modulation transfer functions (MTF) for the system of FIG. 11, with wavefront coding, both with and without filtering.
  • MTF modulation transfer functions
  • FIG. 15 a illustrates transverse ray intercept curves as typically implemented in traditional imaging systems.
  • FIG. 15 b shows MTFs for the system of FIG. 15 a.
  • FIG. 16 illustrates an example of a one dimensional separable filter for use as a post processing element in the present invention.
  • FIG. 17 illustrates the magnitude of the transfer function of the filter of FIG. 16.
  • FIG. 1 shows a single-lens miniature imaging system 100 according to the present invention.
  • Lens 102 includes wavefront coding element 104 formed on its second surface.
  • Detector 106 is preceded by an IR filter 108 and cover glass 110 .
  • Post processor 112 performs processing on the images captured by detector 106 .
  • the example single-lens imaging system (singlet) 100 is designed to meet the following specifications:
  • the example singlet 100 without Wavefront Coding 104 , was designed so that the aberrations that are not corrected by the optical surfaces, namely petzval curvature and axial chromatic aberration, are a type of misfocus.
  • petzval curvature is a type of misfocus with field angle
  • axial chromatic aberration is misfocus with illumination wavelength.
  • the effect of these aberrations could hypothetically be corrected within small regions of the image plane by changing the focus position.
  • the resulting modulation transfer functions (MTFs) and point spread functions (PSFs) will be insensitive to the focus-like aberrations.
  • the MTFs and PSFs will not be the same as an ideal in-focus MTF or PSF from a traditional imaging system.
  • Image processing is required to restore the spatial character of the image and produce a sharp and clear image.
  • Wavefront Coding surface is rectangularly separable and allows for fast processing.
  • Other forms of Wavefront Coding surfaces are non-separable, and the sum of rectangularly separable forms.
  • One non-separable form is defined as:
  • Wavefront Coding surface for singlet 100 in this example is placed at the stop surface (surface 104 ) and has the parameterized equation:
  • FIGS. 2 - 4 illustrate the performance of system 100 with wavefront coding element 104 removed, in order to illustrate design requirements and performance.
  • FIG. 5 illustrates the performance of system 100 with wavefront coding element 104 in place, but without post processing filter 112 .
  • FIG. 6 illustrates the performance improvement with post processing 112 .
  • FIGS. 7 a and 7 b shows point spread functions for system 100 with both wavefront coding and post processing.
  • FIG. 2 illustrates a series of transverse ray intercept curves illustrating aberrations at various wavelengths, for the system of FIG. 1 with wavefront coding surface 104 removed for illustrative purposes. Curves are shown for system 100 at half field angles of 0°, 10°, 20°, and 25° off axis, and for illumination wavelengths of 450 nm, 550 nm, and 650 nm. A slope of zero indicates an in-focus condition. Thus on-axis rays are nearly in focus. But, for off axis field angles, the slopes of the transverse ray intercept curves increase dramatically.
  • FIG. 15 a illustrates traditional transverse ray plots. These plots are taken from “Practical Computer Aided Lens Design”, Gregory Hallick Smith, William Bell, Inc., Richmond 1998. Note that the plot for near on axis rays do look similar to straight horizontal lines, and thus produce an in focus image. Refer also to FIG. 15 b which shows associated MTFs for this system. The MTFs for near on axis rays are good.
  • the transverse ray intercept curves of FIG. 2 are essentially straight lines, both on and off axis, and this is a deliberate design goal, because the use of wavefront coding 104 and image processing 112 can bring the captured images into focus, so long as the curves without wavefront coding are essentially straight lines through the origin, even if the lines are significantly sloped. The effect of the slope is removed by adding wavefront coding and post processing.
  • the aberration petzval curvature gives rise to transverse ray intercept curves, with slopes that are a function of field angle.
  • Axial chromatic aberration gives rise to ray intercept curves with slopes that are a function of illumination wavelength. From FIG. 2, both of these features are part of the transverse ray intercept curves in this example design.
  • FIG. 3 illustrates distortion curves for system 100 of FIG. 1, with wavefront coding element 104 removed.
  • the distortion is less than 0.2%. If distortion was large enough then additional digital processing might be required to reposition image points into a non-distorted image.
  • Table 1 lists the optical prescription of this lens, again without the Wavefront Coding surface. Units are in mm, and the total length is 4.1 mm. Aspheric terms describe rotationally symmetric forms of r order with order equal to 4, 6, 8, etc.
  • FIG. 4 illustrates modulation transfer functions (MTF) for system 100 of FIG. 1, without wavefront coding element 104 .
  • MTFs correspond to the transverse ray aberration curves of FIG. 2.
  • the MTFs are for half field angles 0, 15, and 25 degrees with wavelengths of 550 nm.
  • the MTFs include the pixel MTF due to the Bayer color filter array detector with six micron pixels and 100% fill factor.
  • the on-axis MTF is essentially diffraction limited.
  • the large drop in MTF off-axis is due to the large amount of petzval curvature that is unavoidable in traditional single lens designs with a large field of view.
  • This singlet without wavefront coding 104 does not meet the MTF specification of greater than 40% modulation at 40 lp/mm for all field angles. But, due to its design for Wavefront Coding, modifying the second surface with a Wavefront Coding surface form 104 will lead to acceptable MTF modulation values when combined with digital processing. By changing the wavefront coding element 104 either more or less sensitivity to misfocus aberrations can be formed.
  • FIG. 5 illustrates modulation transfer functions (MTF) for system 100 of FIG. 1, with wavefront coding element 104 in place, but without post processing 112 .
  • the system is focused at infinity.
  • the half field angles shown are 0, 15, and 25 degrees.
  • the wavelength is 550 nm.
  • These MTFs have very little variation with field angle due to the addition of the Wavefront Coding surface, as compared to FIG. 4.
  • Pixel MTF due to the Bayer CFA has again been included.
  • the Bayer CFA with 6 ⁇ m 100% fill factor pixels has a Nyquist spatial frequency of about 42 lp/mm. Note that there are purposely no zeros in the MTFs below the detector's Nyquist spatial frequency.
  • FIG. 6 illustrates modulation transfer functions (MTF) for system 100 of FIG. 1, with wavefront coding 104 and after processing 112 .
  • MTF modulation transfer functions
  • FIGS. 7 a and 7 b illustrate sampled two-dimensional PSFs for system 100 of FIG. 1, with wavefront coding 104 and after processing 112 .
  • FIG. 7 a shows the processed PSFs when the object is at infinity.
  • FIG. 7 b shows the processed PSFs when the object is at 30 cm. These PSFs are for 550 nm wavelength and half field angles of 0, 15, and 25 degrees. After filtering, these PSFs have nearly ideal shapes. This singlet 100 when combined with wavefront coding and digital filtering thus easily meets the system specifications.
  • processor 112 is a rectangularly separable digital filter. Rectangularly separable filters are more computationally efficient (counting the number of multiply and additions) than full 2D kernel filters. Separable filtering consists of first filtering each row of the image with the 1D row filter and forming an intermediate image. The columns of the intermediate image are then filtered with the 1D column filter to provide the final in-focus image.
  • the separable filter used for this example singlet has the same filters for rows and columns.
  • FIG. 16 illustrates an example of a one dimensional separable filter 112 .
  • Coefficients are represented as real values, but can be quantified into integer values for fixed point computations.
  • the sum of the filter coefficients equals approximately 1.
  • the coefficients were determined with a least squares algorithm by minimizing the squared difference between the filtered wavefront coded OTFs and a desired MTF with a value greater than 40% at 40 lp/mm.
  • the width of the filtered PSFs of FIGS. 7 a and 7 b are also minimized with the least squares algorithm. Changes in the filtered PSFs are minimized in regions away from their central peaks.
  • FIG. 17 illustrates the magnitude of the transfer function of the filter of FIG. 16.
  • the zero spatial frequency value is 1.
  • FIG. 8 shows a low cost microscope objective 800 according to the present invention.
  • Lens 802 is aspheric and has focussing power.
  • Aperture stop 804 includes wavefront coding element 806 . Processing is accomplished by processing block 810 .
  • Wavefront coding microscope objective 800 is designed to meet the following objectives:
  • the depth of field of traditional microscope objectives is described by the numerical aperture (NA) and the imaging wavelength.
  • the wavefront coding objective can have a depth of field that is independent of the NA of the objective.
  • the depth of field can be large enough to introduce prospective distortion to the final images. Regions of the object that are farther from the objective will appear smaller then regions of the object closer to the objective. Both near and far regions can image clearly with a large depth of field. Since the depth of field of traditional objectives is small prospective distortion is not common with traditional objectives, especially with high NA. Prospective distortion can be reduced or eliminating by designing wavefront coding objectives that are telecentric. In telecentric imaging systems the magnification of the object is independent of the distance to the object.
  • FIG. 9 illustrates a series of transverse ray intercept curves illustrating aberrations at various wavelengths, for system 800 of FIG. 8, with wavefront coding element 806 removed.
  • the ray intercept curves of FIG. 9 describe the performance of the system at wavelengths 450, 550, and 650 nm for the image field heights of on-axis (0.0 mm), 1.2 mm, and 2.8 mm. Full scale is +/ ⁇ 100 microns. Notice that each of these ray intercept curves vary mainly in slope, as required by the present invention. I.e., the shape of the curves are essentially the same when the slope components of the curves are not considered. While these plots are not quite as close to perfectly straight lines as those in FIG. 2, they can still be considered to be sloped substantially straight lines.
  • Wavefront coding element 806 is placed at aperture stop 804 , and is given by the rectangularly separable form of:
  • FIG. 10 illustrates modulation transfer functions (MTF) for system 800 of FIG. 8, without wavefront coding, with wavefront coding, and with both wavefront coding and post processing filtering, for illumination at 450 nm.
  • Image field heights are 0.0 mm, 1.2 mm, and 2.8 mm.
  • FIG. 11 shows a passive athermalized IR imaging system 1100 according to the present invention.
  • Lens 1102 is composed of silicon.
  • Lens 1104 is composed of germanium.
  • Lens 1106 is composed of silicon.
  • the aperture stop 1108 is at the back surface of lens 1106 .
  • Wavefront coding surface 1110 is on the back surface of lens 1106 (at aperture stop 1108 ).
  • Processing block 1112 processes the image.
  • Wavefront Coding surface for IR system 100 of this example has the parameterized equation:
  • FIG. 12 illustrates a series of transverse ray intercept curves illustrating aberrations at various wavelengths, for system 1100 of FIG. 11, with wavefront coding element 1110 removed.
  • the ray intercept curves of FIG. 11 describe the performance of system 1100 at a wavelength of 10 microns, on axis field points for ambient temperatures of +20° C., ⁇ 20° C., and +70° C. Full scale is +/ ⁇ 100 microns. Again these plots can be considered to be substantially straight lines. While they have more “wiggle” than the plots of FIGS. 2 and 9, in each case, if the plot were fitted to the closest straight line, the wiggles would not stray far from the line.
  • FIG. 13 illustrates on-axis MTF curves for system 1100 without wavefront coding at three temperatures +20° C. ⁇ 20° C., and +70° C.). Performance is nearly diffraction limited at +20°, but drops dramatically with changes in temperature.
  • FIG. 14 illustrates MTFs for system 1100 of FIG. 11, with wavefront coding, both with and without filtering by processing block 1112 .
  • the illumination wavelength is 10 microns.
  • the MTFs without filtering are significantly different from diffraction limited MTFs, but vary little with temperature. Thus, processing block 1112 is able to correct the images.
  • the MTFs after filtering are near diffraction limited for all three temperatures (+20°, ⁇ 20°, and +70°). Filtered MTFs extend only to the Nyquist frequency of the 20 micron detector, or 25 lp/mm.
  • FIG. 10 also illustrates this concept.
  • the MTF curves without wavefront coding do not track each other.
  • the curves with wavefront coding are very close together.
  • the curves with wavefront coding after post processing are very good.
  • transverse ray intercept curves may have noticeable deviations from a straight line (corresponding to the higher spatial frequencies)
  • the transverse ray intercept curves are still “substantially straight lines” according to our definition, because the MTFs with wavefront coding are very close together.
  • the MTFs under consideration are those that correspond to the useful range of the particular system being considered.

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US09/747,788 1995-02-03 2000-12-22 Wavefront coded imaging systems Abandoned US20020118457A1 (en)

Priority Applications (8)

Application Number Priority Date Filing Date Title
US09/747,788 US20020118457A1 (en) 2000-12-22 2000-12-22 Wavefront coded imaging systems
PCT/US2001/044159 WO2002052331A2 (fr) 2000-12-22 2001-11-14 Systèmes d'imagerie à surface d'onde codée
EP01272457A EP1346251A2 (fr) 2000-12-22 2001-11-14 Syst mes d'imagerie surface d'onde cod e
AU2002219861A AU2002219861A1 (en) 2000-12-22 2001-11-14 Wavefront coded imaging systems
US10/407,708 US6940649B2 (en) 1995-02-03 2003-04-04 Wavefront coded imaging systems
US11/192,572 US7106510B2 (en) 1995-02-03 2005-07-29 Wavefront coded imaging systems
US11/511,023 US7554732B2 (en) 1995-02-03 2006-08-28 Wavefront coded imaging systems
US11/511,022 US7554731B2 (en) 1995-02-03 2006-08-28 Wavefront coded imaging systems

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US09/747,788 US20020118457A1 (en) 2000-12-22 2000-12-22 Wavefront coded imaging systems

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US09/070,969 Continuation-In-Part US7218448B1 (en) 1995-02-03 1998-05-01 Extended depth of field optical systems

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US10/407,708 Continuation US6940649B2 (en) 1995-02-03 2003-04-04 Wavefront coded imaging systems

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US10/407,708 Expired - Lifetime US6940649B2 (en) 1995-02-03 2003-04-04 Wavefront coded imaging systems
US11/192,572 Expired - Lifetime US7106510B2 (en) 1995-02-03 2005-07-29 Wavefront coded imaging systems
US11/511,022 Expired - Lifetime US7554731B2 (en) 1995-02-03 2006-08-28 Wavefront coded imaging systems
US11/511,023 Expired - Lifetime US7554732B2 (en) 1995-02-03 2006-08-28 Wavefront coded imaging systems

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US11/192,572 Expired - Lifetime US7106510B2 (en) 1995-02-03 2005-07-29 Wavefront coded imaging systems
US11/511,022 Expired - Lifetime US7554731B2 (en) 1995-02-03 2006-08-28 Wavefront coded imaging systems
US11/511,023 Expired - Lifetime US7554732B2 (en) 1995-02-03 2006-08-28 Wavefront coded imaging systems

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US20050264886A1 (en) 2005-12-01
EP1346251A2 (fr) 2003-09-24
US20040004766A1 (en) 2004-01-08
AU2002219861A1 (en) 2002-07-08
US20070076296A1 (en) 2007-04-05
US7106510B2 (en) 2006-09-12
US7554732B2 (en) 2009-06-30
US7554731B2 (en) 2009-06-30
US6940649B2 (en) 2005-09-06
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WO2002052331A2 (fr) 2002-07-04
US20060291058A1 (en) 2006-12-28

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