Abstract

High pixel count apertures for digital holography may be synthesized by scanning smaller aperture detector arrays. Characterization and compensation for registration errors in the detector array position and pitch and for phase instability between the reference and object field is a major challenge in scanned systems. We use a secondary sensor to monitor phase and image-based registration parameter estimators to demonstrate near diffraction-limited resolution from a 63.4 mm aperture synthesized by scanning a 5.28 mm subaperture over 144 transverse positions. We demonstrate 60 μm resolution at 2 m range.

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  1. C. W. Sherwin, P. Ruina, and R. D. Rawcliffe, “Some early developments in synthetic aperture radar systems,” IRE Trans. Mil. Electron. 6, 111–115 (1962).
    [CrossRef]
  2. L. G. Brown, “A survey of image registration techniques,” ACM Comput. Surv. 24, 4 (1992).
    [CrossRef]
  3. L. Romero and F. Calderon, A Tutorial on Parametric Image Registration (I-Tech, 2007).
  4. J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. 27, 24, 2179–2181 (2002).
    [CrossRef]
  5. R. Binet, J. Colineau, and J.-C. Lehureau, “Short-range synthetic aperture imaging at 633 nm by digital holography,” Appl. Opt. 41, 4775–4782 (2002).
    [CrossRef] [PubMed]
  6. J. R. Fienup and J. J. Miller, “Aberration correction by maximizing generalized sharpness metrics,” J. Opt. Soc. Am. A 20, 609–620 (2003).
    [CrossRef]
  7. J. W. Goodman, Speckle Phenomena in Optics - Theory and Applications (Roberts and Company, 2007).
  8. V. Mico, Z. Zalevsky, C. Ferreira, and J. Garca, “Superresolution digital holographic microscopy for three-dimensional samples,” Opt. Express 16, 19260–19270 (2008).
    [CrossRef]
  9. H. Jiang, J. Zhao, J. Di, and C. Qin, “Numerically correcting the joint misplacement of the sub-holograms in spatial synthetic aperture digital Fresnel holography,” Opt. Express 17, 18836–18842 (2009).
    [CrossRef]
  10. J. W. Goodman, Introduction to Fourier Optics , 3rd ed. (Roberts and Company, 2005).
  11. D. J. Brady, Optical Imaging and Spectroscopy (Wiley, 2009).
    [CrossRef]
  12. U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
    [CrossRef]
  13. B. Javidi, P. Ferraro, S.-H. Hong, S. De Nicola, A. Finizio, D. Alfieri, and G. Pierattini, “Three-dimensional image fusion by use of multiwavelength digital holography,” Opt. Lett. 30, 144–146 (2005).
    [CrossRef] [PubMed]
  14. S. T. Thurman and J. R. Fienup, “Phase-error correction in digital holography,” J. Opt. Soc. Am. A 25, 983–994 (2008).
    [CrossRef]
  15. T. M. Kreis, M. Adams, and W. P. O. Jueptner, “Methods of digital holography: a comparison,” Proc. SPIE 3098, 224–233 (1997).
    [CrossRef]
  16. A. Kozmat and C. R. Christensent, “Effects of speckle on resolution,” J. Opt. Soc. Am. 66, 1257–1260 (1976).
    [CrossRef]

2009

2008

2005

2003

2002

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. 27, 24, 2179–2181 (2002).
[CrossRef]

R. Binet, J. Colineau, and J.-C. Lehureau, “Short-range synthetic aperture imaging at 633 nm by digital holography,” Appl. Opt. 41, 4775–4782 (2002).
[CrossRef] [PubMed]

1997

T. M. Kreis, M. Adams, and W. P. O. Jueptner, “Methods of digital holography: a comparison,” Proc. SPIE 3098, 224–233 (1997).
[CrossRef]

1992

L. G. Brown, “A survey of image registration techniques,” ACM Comput. Surv. 24, 4 (1992).
[CrossRef]

1976

1962

C. W. Sherwin, P. Ruina, and R. D. Rawcliffe, “Some early developments in synthetic aperture radar systems,” IRE Trans. Mil. Electron. 6, 111–115 (1962).
[CrossRef]

Adams, M.

T. M. Kreis, M. Adams, and W. P. O. Jueptner, “Methods of digital holography: a comparison,” Proc. SPIE 3098, 224–233 (1997).
[CrossRef]

Alfieri, D.

Binet, R.

Brady, D. J.

D. J. Brady, Optical Imaging and Spectroscopy (Wiley, 2009).
[CrossRef]

Brown, L. G.

L. G. Brown, “A survey of image registration techniques,” ACM Comput. Surv. 24, 4 (1992).
[CrossRef]

Calderon, F.

L. Romero and F. Calderon, A Tutorial on Parametric Image Registration (I-Tech, 2007).

Christensent, C. R.

Colineau, J.

De Nicola, S.

Di, J.

Ferraro, P.

Ferreira, C.

Fienup, J. R.

Finizio, A.

Garca, J.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics - Theory and Applications (Roberts and Company, 2007).

J. W. Goodman, Introduction to Fourier Optics , 3rd ed. (Roberts and Company, 2005).

Hong, S.-H.

Javidi, B.

Jiang, H.

Jueptner, W. P. O.

T. M. Kreis, M. Adams, and W. P. O. Jueptner, “Methods of digital holography: a comparison,” Proc. SPIE 3098, 224–233 (1997).
[CrossRef]

Juptner, W. P. O.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Kozmat, A.

Kreis, T. M.

T. M. Kreis, M. Adams, and W. P. O. Jueptner, “Methods of digital holography: a comparison,” Proc. SPIE 3098, 224–233 (1997).
[CrossRef]

Lehureau, J.-C.

Massig, J. H.

J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. 27, 24, 2179–2181 (2002).
[CrossRef]

Mico, V.

Miller, J. J.

Pierattini, G.

Qin, C.

Rawcliffe, R. D.

C. W. Sherwin, P. Ruina, and R. D. Rawcliffe, “Some early developments in synthetic aperture radar systems,” IRE Trans. Mil. Electron. 6, 111–115 (1962).
[CrossRef]

Romero, L.

L. Romero and F. Calderon, A Tutorial on Parametric Image Registration (I-Tech, 2007).

Ruina, P.

C. W. Sherwin, P. Ruina, and R. D. Rawcliffe, “Some early developments in synthetic aperture radar systems,” IRE Trans. Mil. Electron. 6, 111–115 (1962).
[CrossRef]

Schnars, U.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Sherwin, C. W.

C. W. Sherwin, P. Ruina, and R. D. Rawcliffe, “Some early developments in synthetic aperture radar systems,” IRE Trans. Mil. Electron. 6, 111–115 (1962).
[CrossRef]

Thurman, S. T.

Zalevsky, Z.

Zhao, J.

ACM Comput. Surv.

L. G. Brown, “A survey of image registration techniques,” ACM Comput. Surv. 24, 4 (1992).
[CrossRef]

Appl. Opt.

IRE Trans. Mil. Electron.

C. W. Sherwin, P. Ruina, and R. D. Rawcliffe, “Some early developments in synthetic aperture radar systems,” IRE Trans. Mil. Electron. 6, 111–115 (1962).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Meas. Sci. Technol.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

T. M. Kreis, M. Adams, and W. P. O. Jueptner, “Methods of digital holography: a comparison,” Proc. SPIE 3098, 224–233 (1997).
[CrossRef]

Other

J. W. Goodman, Speckle Phenomena in Optics - Theory and Applications (Roberts and Company, 2007).

L. Romero and F. Calderon, A Tutorial on Parametric Image Registration (I-Tech, 2007).

J. W. Goodman, Introduction to Fourier Optics , 3rd ed. (Roberts and Company, 2005).

D. J. Brady, Optical Imaging and Spectroscopy (Wiley, 2009).
[CrossRef]

Supplementary Material (1)

» Media 1: MOV (2366 KB)     

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Figures (10)

Fig. 1
Fig. 1

Schematic for image-based synthetic aperture holography: (a) scattered field Es and reference field R form a hologram in the detector plane by propagating the distances, zd and zr , respectively, and (b) dynamic camera scans patch by patch within a reinitialized block. Note that Ãi j describes the error-impacted measurement of a measurement subset Ai j .

Fig. 2
Fig. 2

Flow chart of the error estimation processes for image-based synthetic aperture holography. The estimated errors are denoted in the processes.

Fig. 3
Fig. 3

Experimental setup: (a) the field generation consists of a HeNe (633 nm laser), M (mirrors), BS1–5 (beam splitters), AF (1951 USAF resolution target), OBJ+P (microscopic objective lens and pinhole), and L (lens), and (b) photographs of the field generation system (left) and the field detection system (right). Object 1 is a performance test object and Object 2 is a depth imaging object.

Fig. 4
Fig. 4

Piston phase correlation in two distant cameras: the red continuous line is the relative phase variation of camera 1 and the blue dotted line is the relative phase variation of camera 2.

Fig. 5
Fig. 5

Evolution of estimation effects on the guiding features image: the left and right hand guiding features of (a) the raw data image, (b) the piston phase compensated image, (c) the hologram block synthesized image, (d) the WA hologram synthesized image, (e) the zoomed-in image of (d), and (f) the zoomed-in image of reference field estimated image. Also, (g) the estimated reference field discrepancy. Note that the image pixel resolution is 4.4 μm in the angular spectrum method.

Fig. 6
Fig. 6

Resolution improvement to the number of hologram patches in the guiding features: (a), (b), and (c) show the images of 1×1, 3×3, and 12×12 hologram patches in the left-hand AF targets. Also, (d), (e), and (f) show the images of 1×1, 3×3, and 12×12 hologram patches in the right-hand AF targets.

Fig. 7
Fig. 7

(Media 1) Zoom-in movie starts from a full FOV image at 63.4 × 63.4 mm to a zoomed-in image at 2.1 × 2.1 mm. The zoomed image focuses on the CPU chip.

Fig. 8
Fig. 8

The images of the AF targets in the depth imaging experiment: (a) left-hand guiding features, (b) performance test features, and (c) right-hand guiding features of the raw data. Also, (d) left-hand guiding features, (e) performance test features, and (f) right-hand guiding features of the hologram synthesis.

Fig. 9
Fig. 9

The image of the CPU chip: resolution improvement to the number of hologram patches showing the images of (a) the 1×1 hologram patch, (b) the 3×3 hologram patches, and (c) the 12×12 hologram patches. Also, comparison of the images of (d) the un-synthesized hologram, (e) the synthesized hologram, and (f) the real photograph. Note that this object is placed 44 mm closer to the detector plane than the guiding features’ plane.

Fig. 10
Fig. 10

The monitored piston phase variation of scanned 144 hologram patches.

Tables (2)

Tables Icon

Table 1 The estimated parameters of the detector registration errors and the reference field errors for the WA hologram synthesis.

Tables Icon

Table 2 The Chebychev coefficients for the reference field discrepancy.

Equations (32)

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E s ( u , v ; z d ) = ( E 0 h ) ( u , v ; z d ) = E o ( x , y ) h ( u x , v y ; z d ) d x d y ,
h ( u , v ; z ) = [ j z / λ z 2 + u 2 + v 2 + z / 2 π ( z 2 + u 2 + v 2 ) 3 / 2 ] e j 2 π λ z 2 + u 2 + v 2 ,
𝒡 { h ( u , v ; z ) } = e j 2 π z λ 1 ( λ f u ) 2 ( λ f v ) 2 .
I ( u , v ; z d , z r ) = | R ( u , v ; z r ) + E s ( u , v ; z d ) | 2 ,
I i j ( u , v ; z d , z r ) = | R i j ( u , v ; z r ) + E s i j ( u , v ; z d ) | 2 , ( u , v ) A i j = | R i j ( u , v ; z r ) | 2 + | E s i j ( u , v ; z d ) | 2
+ R * , i j ( u , v ; z r ) E s i j ( u , v ; z d ) + R i j ( u , v ; z r ) E s * , i j ( u , v ; z d ) ,
D ˜ i j ( u , v ; z d , z r ) = D i j ( u , v ; z d , z r ; θ e i j ) = e j φ c i j R ˜ * , i j ( u , v ; z r ) E ˜ s i j ( u , v ; z d ) e j φ r i j ( u , v ) .
R ˜ i j ( u , v ; z r ) = h ( u , v ; z r ) δ ( u + e d , u i j + e f , u i j , v + e d , v i j + e f , v i j ; z r ) = h ( u , v ; z r ) δ ( u + e t , u i j , v + e t , v i j ; z r )
E ˜ s i j ( u , v ; z d ) = E s i j ( u + e d , u i j , v + e d , v i j ; z d ) = [ E i ( x , y ) E o ( x , y ) ] h ( u , v ; z d ) δ ( u + e d , u i j , v + e d , v i j ; z d ) .
θ e i j = [ e d p i j , e d b i j , e t i j , φ r i j ( u , v ) ] T ,
θ e i j = [ e d b i j , e t i j , φ t i j ( u , v ) ] T .
θ e i j = [ φ r i j ( u , v ) ] T .
φ c i j = angle { u v sign { s i j ( u , v ) / s 11 ( u , v ) } } ,
E o m n ( x , y ; e d p , u , e d p , v ) = 𝒡 1 { 𝒡 { R m n ( u , v ; z r ) × D ˜ m n ( u e d p , u , v e d p , v ; z d , z r ) } e j z d k 2 k u 2 k v 2 } ,
Ω S M ( e d p ) = x y G I ( x , y ; e d p ) 0.5 ,
e d p = [ e d p , u 11 , e d p , v 11 , , e d p , u I J , e d p , v I J ] T ,
e ^ d p = arg min e d p Ω S M ( e d p ) .
D ( u , v ; z d , z r ) = m n D ˜ m n ( u e d b , u m n , v e d b , v m n ; z d , z r ) .
R ( u , v ; z r ) = m n R ˜ m n ( u e t , u m n , v e t , v m n ; z r ) .
E s ( u , v ; e d b , u , e d b , v , e t , u , e t , v ) = R ˜ ( u e t , u , v e t , v ; z r ) × D ˜ ( u e b d , u , v e d b , v ; z d , z r )
E o ( x , y ; e d b , u , e d b , v , e t , u , e t , v ) = 𝒡 1 { 𝒡 { E s ( u , v ; e d b , u , e d b , v , e t , u , e t , v ) } × e j z d k 2 k u 2 k v 2 } .
Ω S M ( e d b , r ) = x y G I ( x , y ; e d b , r ) 0.5 ,
e d b , r = [ e d b , u 11 , e d b , v 11 , e t , u 11 , e t , v 11 , e d b , u M N , e d b , v M N , e t , u M N , e t , v M N ] T .
e ^ d b , r = arg min e d b , r Ω S M ( e d b , r ) .
φ r ( u , v ; C k ) = k C k P k ( u , v ) ,
E o ( x , y ; C k ) = 𝒡 1 { 𝒡 { e j φ r ( u , v ) E s ( u , v ; z d ) } e j z d k 2 k u 2 k v 2 } .
Ω S M ( C k ) = x y G I ( x , y ; C k ) 0.5 ,
C ^ k = arg min C k Ω S M ( C k ) ,
δ x = λ z N δ u ,
Δ x = λ z δ u ,
δ x eff = δ u ,
Δ x eff = N δ u .

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