Abstract

This paper considers some of the most important optical parameters that characterize a digital holographic microscope (DHM) and presents their mathematical derivation based on geometrical and diffraction-based models. It supports and justifies the use of the out-of-focus recording of holograms by showing that the field of view can be increased when recording the hologram in front of the in-focus image plane. In this manner a better match between the space–bandwidth product (SBP) of the microscope objective and that of the reconstructed hologram can be obtained. Hence, DHM offers a more cost-efficient way to increase the recorded SBP compared to the application of a high-quality microscope objective (large numerical aperture and low magnification) used in conventional microscopy. Furthermore, an expression for the imaging distance (distance between hologram and image plane), while maintaining the optical resolution and sufficient sampling, is obtained. This expression takes into account all kinds of reference-wave curvature and can easily be transferred to lensless digital holography. In this context it could be demonstrated that an object wave matched reference wave offers a significantly smaller imaging distance and hence the largest recoverable SBP. In addition, a new, to our knowledge, approach, based on the influence of defocus on the modulation transfer function, is used to derive the depth of field (DOF) for a circular aperture (lens-based system) and a rectangular aperture (lensless system), respectively. This investigation leads to the finding that a rectangular aperture offers an increased resolution combined with an increased DOF, when compared to a circular aperture of the same size.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  3. B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. J. Magistretti, “Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy,” Opt. Express 13, 9361–9373 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  31. J. Pawley, ed., Handbook of Biological Confocal Microscopy (Springer, 2006).

2012 (1)

2011 (2)

2009 (1)

2008 (1)

J. Kuehn, F. Charriére, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

2006 (2)

2005 (1)

2004 (2)

2003 (1)

2002 (1)

2001 (2)

I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt. 40, 6177–6186 (2001).
[CrossRef]

S. Coëtmellec, C. Buraga-Lefebvre, D. Lebrun, and C. Ozkul, “Application of in-line digital holography to multiple plane velocimetry,” Meas. Sci. Technol. 12, 1392–1397 (2001).
[CrossRef]

1997 (1)

T. M. Kreis and W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360(1997).
[CrossRef]

1994 (1)

P. Whittaker, R. A. Kloner, D. R. Boughner, and J. G. Pickering, “Quantitative assessment of myocardial collagen with picrosirius red staining and circularly polarized light,” Basic Res. Cardiol. 89, 397–410 (1994).
[CrossRef]

Aspert, N.

Bally, G. v.

Borbély, V.

Boughner, D. R.

P. Whittaker, R. A. Kloner, D. R. Boughner, and J. G. Pickering, “Quantitative assessment of myocardial collagen with picrosirius red staining and circularly polarized light,” Basic Res. Cardiol. 89, 397–410 (1994).
[CrossRef]

Bourquin, S.

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, 2000).

Bryanston-Cross, P.

Bryant, R.

M. A. Schulze, M. A. Hunt, E. Voelkl, J. D. Hickson, W. R. Usry, R. G. Smith, R. Bryant, and C. J. Thomas, “Semiconductor wafer defect detection using digital holography,” in Process and Materials Characterization and Diagnostics in IC Manufacturing (SPIE, 2003), pp. 183–193.

Buah-Bassuah, P.

P. Ferraro, L. Miccio, S. Grilli, R. Meucci, S. D. Nicola, and P. Buah-Bassuah, “Infrared digital holographic imaging,” SPIE Newsroom (2008), http://spie.org/x19497.xml.

Buraga-Lefebvre, C.

S. Coëtmellec, C. Buraga-Lefebvre, D. Lebrun, and C. Ozkul, “Application of in-line digital holography to multiple plane velocimetry,” Meas. Sci. Technol. 12, 1392–1397 (2001).
[CrossRef]

Carl, D.

Cathey, W. T.

Charriére, F.

Claus, D.

Coëtmellec, S.

S. Coëtmellec, C. Buraga-Lefebvre, D. Lebrun, and C. Ozkul, “Application of in-line digital holography to multiple plane velocimetry,” Meas. Sci. Technol. 12, 1392–1397 (2001).
[CrossRef]

Colomb, T.

Cuche, E.

Czitrovszky, A.

Demoli, N.

Depeursinge, C.

Dowski, E. R.

Emery, Y.

J. Kuehn, F. Charriére, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. J. Magistretti, “Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy,” Opt. Express 13, 9361–9373 (2005).
[CrossRef]

Ferraro, P.

P. Ferraro, L. Miccio, S. Grilli, R. Meucci, S. D. Nicola, and P. Buah-Bassuah, “Infrared digital holographic imaging,” SPIE Newsroom (2008), http://spie.org/x19497.xml.

Füzessy, Z.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Grilli, S.

P. Ferraro, L. Miccio, S. Grilli, R. Meucci, S. D. Nicola, and P. Buah-Bassuah, “Infrared digital holographic imaging,” SPIE Newsroom (2008), http://spie.org/x19497.xml.

Gusev, M. E.

Gyímesi, F.

Haferkorn, H.

H. Haferkorn, Optik, Physikalisch-technische Grunlagen und Anwendungen (Willey-VCH, 2003).

Harmati, I.

Hecht, E.

E. Hecht, Optics (Addison Wesley, 1998).

Hickson, J. D.

M. A. Schulze, M. A. Hunt, E. Voelkl, J. D. Hickson, W. R. Usry, R. G. Smith, R. Bryant, and C. J. Thomas, “Semiconductor wafer defect detection using digital holography,” in Process and Materials Characterization and Diagnostics in IC Manufacturing (SPIE, 2003), pp. 183–193.

Humphry, M. J.

Hunt, M. A.

M. A. Schulze, M. A. Hunt, E. Voelkl, J. D. Hickson, W. R. Usry, R. G. Smith, R. Bryant, and C. J. Thomas, “Semiconductor wafer defect detection using digital holography,” in Process and Materials Characterization and Diagnostics in IC Manufacturing (SPIE, 2003), pp. 183–193.

Iliescu, D.

D. Claus, D. Iliescu, and P. Bryanston-Cross, “Quantitative space-bandwidth product analysis in digital holography,” Appl. Opt. 50, H116–H127 (2011).
[CrossRef]

D. Claus, D. Iliescu, J. Watson, and J. Rodenburg, “Comparison of different digital holographic setup configurations,” in Digital Holography and Three-Dimensional Imaging (DH) 2012 (OSA, 2012), p. DM4C.3.

Jueptner, W.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

Jüptner, W.

S. Seebacher, W. Osten, and W. Jüptner, “Measuring shape and deformation of small objects using digital holography,” in SPIE Conference on Laser interferometry IX: Applications (SPIE, 1998), pp. 104–115.

Jüptner, W. P. O.

T. M. Kreis and W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360(1997).
[CrossRef]

Kato, J.

Kemper, B.

Kloner, R. A.

P. Whittaker, R. A. Kloner, D. R. Boughner, and J. G. Pickering, “Quantitative assessment of myocardial collagen with picrosirius red staining and circularly polarized light,” Basic Res. Cardiol. 89, 397–410 (1994).
[CrossRef]

Kreis, T. M.

T. M. Kreis and W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360(1997).
[CrossRef]

Kuehn, J.

J. Kuehn, F. Charriére, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

Kühn, J.

Lebrun, D.

S. Coëtmellec, C. Buraga-Lefebvre, D. Lebrun, and C. Ozkul, “Application of in-line digital holography to multiple plane velocimetry,” Meas. Sci. Technol. 12, 1392–1397 (2001).
[CrossRef]

Lotfi, A.

Magistretti, P. J.

Maiden, A. M.

Marian, A.

Marquet, P.

Mestrovic, J.

Meucci, R.

P. Ferraro, L. Miccio, S. Grilli, R. Meucci, S. D. Nicola, and P. Buah-Bassuah, “Infrared digital holographic imaging,” SPIE Newsroom (2008), http://spie.org/x19497.xml.

Miccio, L.

P. Ferraro, L. Miccio, S. Grilli, R. Meucci, S. D. Nicola, and P. Buah-Bassuah, “Infrared digital holographic imaging,” SPIE Newsroom (2008), http://spie.org/x19497.xml.

Mizuno, J.

Molnár, G.

Molnárka, G.

Montfort, F.

Nagy, A.

Nagy, A. T.

Nicola, S. D.

P. Ferraro, L. Miccio, S. Grilli, R. Meucci, S. D. Nicola, and P. Buah-Bassuah, “Infrared digital holographic imaging,” SPIE Newsroom (2008), http://spie.org/x19497.xml.

Ohta, S.

Osten, W.

G. Pedrini, W. Osten, and M. E. Gusev, “High-speed digital holographic interferometry for vibration measurement,” Appl. Opt. 45, 3456–3462 (2006).
[CrossRef]

S. Seebacher, W. Osten, and W. Jüptner, “Measuring shape and deformation of small objects using digital holography,” in SPIE Conference on Laser interferometry IX: Applications (SPIE, 1998), pp. 104–115.

Ozkul, C.

S. Coëtmellec, C. Buraga-Lefebvre, D. Lebrun, and C. Ozkul, “Application of in-line digital holography to multiple plane velocimetry,” Meas. Sci. Technol. 12, 1392–1397 (2001).
[CrossRef]

Pedrini, G.

Piano, E.

Pickering, J. G.

P. Whittaker, R. A. Kloner, D. R. Boughner, and J. G. Pickering, “Quantitative assessment of myocardial collagen with picrosirius red staining and circularly polarized light,” Basic Res. Cardiol. 89, 397–410 (1994).
[CrossRef]

Pontiggia, C.

Ráczkevi, B.

Rappaz, B.

Repetto, L.

Rodenburg, J.

D. Claus, J. Watson, and J. Rodenburg, “Analysis and interpretation of the Seidel aberration coefficients in digital holography,” Appl. Opt. 50, H220–H229 (2011).
[CrossRef]

D. Claus, D. Iliescu, J. Watson, and J. Rodenburg, “Comparison of different digital holographic setup configurations,” in Digital Holography and Three-Dimensional Imaging (DH) 2012 (OSA, 2012), p. DM4C.3.

Rodenburg, J. M.

Schluesener, H.

Schnars, U.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

Schulze, M. A.

M. A. Schulze, M. A. Hunt, E. Voelkl, J. D. Hickson, W. R. Usry, R. G. Smith, R. Bryant, and C. J. Thomas, “Semiconductor wafer defect detection using digital holography,” in Process and Materials Characterization and Diagnostics in IC Manufacturing (SPIE, 2003), pp. 183–193.

Seebacher, S.

S. Seebacher, W. Osten, and W. Jüptner, “Measuring shape and deformation of small objects using digital holography,” in SPIE Conference on Laser interferometry IX: Applications (SPIE, 1998), pp. 104–115.

Smith, R. G.

M. A. Schulze, M. A. Hunt, E. Voelkl, J. D. Hickson, W. R. Usry, R. G. Smith, R. Bryant, and C. J. Thomas, “Semiconductor wafer defect detection using digital holography,” in Process and Materials Characterization and Diagnostics in IC Manufacturing (SPIE, 2003), pp. 183–193.

Sovic, I.

Sweeney, F. G. R.

Szigethy, D.

Thomas, C. J.

M. A. Schulze, M. A. Hunt, E. Voelkl, J. D. Hickson, W. R. Usry, R. G. Smith, R. Bryant, and C. J. Thomas, “Semiconductor wafer defect detection using digital holography,” in Process and Materials Characterization and Diagnostics in IC Manufacturing (SPIE, 2003), pp. 183–193.

Usry, W. R.

M. A. Schulze, M. A. Hunt, E. Voelkl, J. D. Hickson, W. R. Usry, R. G. Smith, R. Bryant, and C. J. Thomas, “Semiconductor wafer defect detection using digital holography,” in Process and Materials Characterization and Diagnostics in IC Manufacturing (SPIE, 2003), pp. 183–193.

Voelkl, E.

M. A. Schulze, M. A. Hunt, E. Voelkl, J. D. Hickson, W. R. Usry, R. G. Smith, R. Bryant, and C. J. Thomas, “Semiconductor wafer defect detection using digital holography,” in Process and Materials Characterization and Diagnostics in IC Manufacturing (SPIE, 2003), pp. 183–193.

Watson, J.

D. Claus, J. Watson, and J. Rodenburg, “Analysis and interpretation of the Seidel aberration coefficients in digital holography,” Appl. Opt. 50, H220–H229 (2011).
[CrossRef]

D. Claus, D. Iliescu, J. Watson, and J. Rodenburg, “Comparison of different digital holographic setup configurations,” in Digital Holography and Three-Dimensional Imaging (DH) 2012 (OSA, 2012), p. DM4C.3.

Wernike, G.

Whittaker, P.

P. Whittaker, R. A. Kloner, D. R. Boughner, and J. G. Pickering, “Quantitative assessment of myocardial collagen with picrosirius red staining and circularly polarized light,” Basic Res. Cardiol. 89, 397–410 (1994).
[CrossRef]

Yamaguchi, I.

Zhang, F.

Appl. Opt. (8)

Basic Res. Cardiol. (1)

P. Whittaker, R. A. Kloner, D. R. Boughner, and J. G. Pickering, “Quantitative assessment of myocardial collagen with picrosirius red staining and circularly polarized light,” Basic Res. Cardiol. 89, 397–410 (1994).
[CrossRef]

J. Opt. Soc. Am. A (1)

Meas. Sci. Technol. (2)

J. Kuehn, F. Charriére, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

S. Coëtmellec, C. Buraga-Lefebvre, D. Lebrun, and C. Ozkul, “Application of in-line digital holography to multiple plane velocimetry,” Meas. Sci. Technol. 12, 1392–1397 (2001).
[CrossRef]

Opt. Eng. (1)

T. M. Kreis and W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360(1997).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Other (15)

J. Pawley, ed., Handbook of Biological Confocal Microscopy (Springer, 2006).

M. A. Schulze, M. A. Hunt, E. Voelkl, J. D. Hickson, W. R. Usry, R. G. Smith, R. Bryant, and C. J. Thomas, “Semiconductor wafer defect detection using digital holography,” in Process and Materials Characterization and Diagnostics in IC Manufacturing (SPIE, 2003), pp. 183–193.

S. Seebacher, W. Osten, and W. Jüptner, “Measuring shape and deformation of small objects using digital holography,” in SPIE Conference on Laser interferometry IX: Applications (SPIE, 1998), pp. 104–115.

P. Ferraro, A. Wax, and Z. Zalevsky, eds., Coherent Light Microscopy (Springer, 2011).

W. Osten, ed., Optical Inspection of Microsystems (Taylor & Francis, 2006).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

P. Ferraro, L. Miccio, S. Grilli, R. Meucci, S. D. Nicola, and P. Buah-Bassuah, “Infrared digital holographic imaging,” SPIE Newsroom (2008), http://spie.org/x19497.xml.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

D. Claus, D. Iliescu, J. Watson, and J. Rodenburg, “Comparison of different digital holographic setup configurations,” in Digital Holography and Three-Dimensional Imaging (DH) 2012 (OSA, 2012), p. DM4C.3.

E. Hecht, Optics (Addison Wesley, 1998).

O. Lummer and F. Reiche, eds., Die Lehre von der Bildentstehung im Mikroskop, von Ernst Abbe (F. Vieweg, 1910).

H. Haferkorn, Optik, Physikalisch-technische Grunlagen und Anwendungen (Willey-VCH, 2003).

M. Born and E. Wolf, eds., Principles of Optics (Cambridge University, 1999).

D. Malacara, ed., Optical Shop Testing (Wiley-VCH, 2006).

R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, 2000).

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Figures (12)

Fig. 1.
Fig. 1.

ISO 9345-1 normalized parameters for a finite microscope objective.

Fig. 2.
Fig. 2.

Imaging and reconstruction process.

Fig. 3.
Fig. 3.

Schematic diagram of DHM setup.

Fig. 4.
Fig. 4.

Parallel incident beams on a thin lens with ϑ the angle of incidence.

Fig. 5.
Fig. 5.

Schematic sketch of different planes (including nomenclature) and wavefronts involved in the holographic recording process.

Fig. 6.
Fig. 6.

(a) Geometry and nomenclature for circular aperture; (b) cross section for resulting in-focus diffraction pattern; (c) geometry and nomenclature for rectangular aperture; and (d) cross section for resulting in-focus diffraction pattern.

Fig. 7.
Fig. 7.

Geometrical optical DOF.

Fig. 8.
Fig. 8.

Influence of defocus on the MTF of a (a) circular and (b) rectangular apertures.

Fig. 9.
Fig. 9.

Graphical representation of interference between object wave and reference wave; their source point location and the recording location (detector edge) result in the largest phase gradient.

Fig. 10.
Fig. 10.

(a) Minimum imaging distance dimage as a function of the ratio between the reference-wave source point distant d˜ref and recording distance d˜2 and (b) minimum imaging distance for plane and matched spherical reference wave as a function of the ratio between the detector’s pixel size Δx and the imaged smallest resolvable object detail δβ, for setup specifications used in the experiments (N=3000, λ=632.8nm, β=20, and NA=0.4).

Fig. 11.
Fig. 11.

(a) Numerical reconstruction without suppression of parabolic phase term; (b) with suppression and residual phase tilt; and (c) with parabolic phase and phase-tilt suppression.

Fig. 12.
Fig. 12.

Numerical reconstruction of holograms recorded (a) behind the image plane and (b) in front of the image plane. Comparison of experimentally obtained data and calculated data for image sizes in (c) x- and (d) y-directions.

Tables (1)

Tables Icon

Table 1. Evaluation of the Experimentally Obtained Data

Equations (45)

Equations on this page are rendered with MathJax. Learn more.

x+ximaged1=ximagefd1=(x+ximage)fy=(1+β)fβ,x+ximaged2=xfd2=(x+ximage)fy=(1+β)f,
f=f=β(d1+d2)(1+β)2=β195mm(1+β)2.
D=2d2tan(ε)=2d2tan[asin(NAβ)]=195mm·2ββ+1tan[asin(NAβ)]390mm·NAβ+1.
x1=f(tanϑtanκT).
dr=x1tanκT=f(tanϑtanκT1)=fx1ftanϑx1.
dfb=x1tanϑ=f(1tanκTtanϑ)=f(1drtanϑx1).
u(x)=exp(i2πd˜2λ)iλd˜2uL2(x˜)exp[iπλd˜2(x˜x)2]dx˜,
uL2(x˜)=exp[iπλx˜2(1d11f2)]exp[iπλx¯2(1d01f1)]exp(i2πx¯xλd0)dx¯×u(x)exp[iπλx2(1d0+1d1)]exp(2iπλd1x˜x)dx=exp[iπλx˜2(1d11f2)]F{u(x)},
u(x)=|λd1|exp(iπλd˜2x2)exp[iπλx˜(x˜d1+x˜d˜2x˜f22xd˜2)]δ(x˜)dx˜=|λd1|exp(iπλd˜2x2).
φ(x,y)=π(x2+y2)λdrefd˜2drefd˜2=π(x2+y2)λ1dparab,
φramp=2π(kNsx+lMsy)=2πλdref(kΔxxref+lΔyyref),
I(ε)I0=[2J1(πDλsinε)sinε]2,
sinε=rlrrld.
δ=1.22λrD=0.61λNA1.22λdD.
δ1.22λfD.
I(α,γ)I0=(sinαα)2(sinγγ)2.
α=πXxλr,γ=πYyλr,
δ=λrX=0.5λNA.
DOF=DOFλ+DOFg.
tanε1=Δx2DOFlg=X2(d+DOFlg),tanε2=Δx2DOFrg=X2(dDOFrg).
DOFg=DOFlg+DOFrg=ΔxdXΔx+ΔxdX+Δx=2ΔxdXX2Δx2.
DOFg=2ΔxdXβ(X2Δx2β2)2ΔxdβX=ΔxβNA.
φ(x,y)=2πλW(x,y)=8πWmax(x˜,y˜)λx˜2+y˜2D2,
Wmaxλ=12λ(1da1di)(D2)2=12λ(1di+Δz1di)(D2)2,
0.5n2λNA2di=Δzdi+Δz;fordiΔzit follows that0.5n2λNA2=Δz.
DOFλ=±0.5nλ0NA2,
DOFλ=±0.8nλ0NA2,
NA=nX2di.
x=xδx=NΔx(1dimaged2+dimagef),
N=N(1dimaged2+dimagef).
x=xβ=NΔxβ(1dimaged2+dimagef).
FOV=x×y=NΔx×MΔy[1β(1dimaged2+dimagef)]2.
uref(x)=Arefexp[iπλdref(xxref)2],uL(x)=ALexp[iπλd˜2(xxL)2].
φ=πλx2(1d˜21dref)2πλx(x˜maxd˜2xrefdref)+πλ(x˜max2d˜2xref2dref)=πλΔx2k2(1d˜21dref)2πλΔxk(x˜maxd˜2xrefdref)+πλ(x˜max2d˜2xref2dref).
ΔφΔkφk=2πλΔx2k(1d˜21dref)2πλΔx(x˜maxd˜2xrefdref)+πλ(x˜max2d˜2xref2dref).
d˜2>(NΔx22Δxx˜max)drefλdref+NΔx22Δxxref.
d˜ref=dref+dimage=dref+d˜2d2.
d˜2>λ(d2dref)+2Δx(xrefx˜max)2λ±[λ(d2dref)+2Δx(xrefx˜max)2λ]2+(NΔx22Δxx˜max)(drefd2)λ.
dimage>λ(d2dref)+ΔxD2λ+[λ(d2dref)2λ]2+(NΔx2+ΔxD)(drefd2)λd2,
d2=195mm·ββ+1.
tanα=D+NΔx2d˜2=2xref+NΔx2d˜ref.
xref=(D+NΔx)d˜refNΔxd˜22d˜2=(D+NΔx)(dref+d˜2d2)NΔxd˜22d˜2.
dimage>λ(d2dref)+2ΔxD2λ+[λ(d2dref)+2ΔxD2λ]2+2(NΔx2+DΔx)(drefd2)λd2.
dimage>{DΔxλd2in-line,2DΔxλd2off-axis.
dimage>{(D+NΔx)Δxλd2in-line,2(D+NΔx)Δxλd2off-axis.

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