Abstract

This research images trapped atoms in three dimensions, utilizing light field imaging. Such a system is of interest in the development of atom interferometer accelerometers in dynamic systems where strictly defined focal planes may be impractical. In this research, a light field microscope was constructed utilizing a Lytro Development Kit micro lens array and sensor. It was used to image fluorescing rubidium atoms in a magneto optical trap. The three-dimensional (3D) volume of the atoms is reconstructed using a modeled point spread function (PSF), taking into consideration that the low magnification (1.25) of the system changed typical assumptions used in the optics model for the PSF. The 3D reconstruction is analyzed with respect to a standard off-axis fluorescence image. Optical axis separation between two atom clouds is measured to a 100 μm accuracy in a 3 mm deep volume, with a 16 μm in-focus standard resolution with a 3.9 mm by 3.9 mm field of view. Optical axis spreading is observed in the reconstruction and discussed. The 3D information can be used to determine properties of the atom cloud with a single camera and single image, and can be applied anywhere 3D information is needed but optical access may be limited.

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References

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  1. S. M. Dickerson, J. M. Hogan, A. Sugarbaker, D. M. Johnson, and M. A. Kasevich, “Multiaxis inertial sensing with long-time point source atom interferometry,” Phys. Rev. Lett. 111, 083001 (2013).
    [Crossref]
  2. J. Burke, B. Deissler, K. Hughes, and C. Sackett, “Confinement effects in a guided-wave atom interferometer with millimeter-scale arm separation,” Phys. Rev. A 78, 023619 (2008).
    [Crossref]
  3. K. D. Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nat. Phys. 3, 556–560 (2007).
    [Crossref]
  4. G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. Theor. Appl. 7, 821–825 (1908).
    [Crossref]
  5. E. H. Adelson and J. Y. A. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992).
    [Crossref]
  6. R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” (2005).
  7. M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25, 924–934 (2006).
    [Crossref]
  8. M. Broxton, L. Grosenick, S. Yang, N. Cohen, A. Andalman, K. Deisseroth, and M. Levoy, “Wave optics theory and 3-d deconvolution for the light field microscope,” Opt. Express 21, 25418–25439 (2013).
    [Crossref]
  9. N. Cohen, S. Yang, A. Andalman, M. Broxton, L. Grosenick, K. Deisseroth, M. Horowitz, and M. Levoy, “Enhancing the performance of the light field microscope using wavefront coding,” Opt. Express 22, 24817–24839 (2014).
    [Crossref]
  10. K. Sakmann and M. Kasevich, “Single-shot three-dimensional imaging of dilute atomic clouds,” Opt. Lett. 39, 5317–5320 (2014).
    [Crossref]
  11. L. Mignard-Debise and I. Ihrke, “Light-field microscopy with a consumer light-field camera,” in International Conference on 3D Vision (3DV) (IEEE, 2015), pp. 335–343.
  12. M. Gu, Advanced Optical Imaging Theory (Springer, 2000), Vol. 75.
  13. S. R. Deans, The Radon Transform and Some of Its Applications (Courier Corporation, 2007).
  14. J. Hsieh, Computed Tomography: Principles, Design, Artifacts, and Recent Advances (SPIE, 2003), Vol. 114.

2014 (2)

2013 (2)

S. M. Dickerson, J. M. Hogan, A. Sugarbaker, D. M. Johnson, and M. A. Kasevich, “Multiaxis inertial sensing with long-time point source atom interferometry,” Phys. Rev. Lett. 111, 083001 (2013).
[Crossref]

M. Broxton, L. Grosenick, S. Yang, N. Cohen, A. Andalman, K. Deisseroth, and M. Levoy, “Wave optics theory and 3-d deconvolution for the light field microscope,” Opt. Express 21, 25418–25439 (2013).
[Crossref]

2008 (1)

J. Burke, B. Deissler, K. Hughes, and C. Sackett, “Confinement effects in a guided-wave atom interferometer with millimeter-scale arm separation,” Phys. Rev. A 78, 023619 (2008).
[Crossref]

2007 (1)

K. D. Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nat. Phys. 3, 556–560 (2007).
[Crossref]

2006 (1)

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25, 924–934 (2006).
[Crossref]

1992 (1)

E. H. Adelson and J. Y. A. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992).
[Crossref]

1908 (1)

G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. Theor. Appl. 7, 821–825 (1908).
[Crossref]

Adams, A.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25, 924–934 (2006).
[Crossref]

Adelson, E. H.

E. H. Adelson and J. Y. A. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992).
[Crossref]

Andalman, A.

Brédif, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” (2005).

Broxton, M.

Burke, J.

J. Burke, B. Deissler, K. Hughes, and C. Sackett, “Confinement effects in a guided-wave atom interferometer with millimeter-scale arm separation,” Phys. Rev. A 78, 023619 (2008).
[Crossref]

Cohen, N.

Deans, S. R.

S. R. Deans, The Radon Transform and Some of Its Applications (Courier Corporation, 2007).

Deisseroth, K.

Deissler, B.

J. Burke, B. Deissler, K. Hughes, and C. Sackett, “Confinement effects in a guided-wave atom interferometer with millimeter-scale arm separation,” Phys. Rev. A 78, 023619 (2008).
[Crossref]

Dickerson, S. M.

S. M. Dickerson, J. M. Hogan, A. Sugarbaker, D. M. Johnson, and M. A. Kasevich, “Multiaxis inertial sensing with long-time point source atom interferometry,” Phys. Rev. Lett. 111, 083001 (2013).
[Crossref]

Duval, G.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” (2005).

Footer, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25, 924–934 (2006).
[Crossref]

Grosenick, L.

Gu, M.

M. Gu, Advanced Optical Imaging Theory (Springer, 2000), Vol. 75.

Hanrahan, P.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” (2005).

Hogan, J. M.

S. M. Dickerson, J. M. Hogan, A. Sugarbaker, D. M. Johnson, and M. A. Kasevich, “Multiaxis inertial sensing with long-time point source atom interferometry,” Phys. Rev. Lett. 111, 083001 (2013).
[Crossref]

Horowitz, M.

N. Cohen, S. Yang, A. Andalman, M. Broxton, L. Grosenick, K. Deisseroth, M. Horowitz, and M. Levoy, “Enhancing the performance of the light field microscope using wavefront coding,” Opt. Express 22, 24817–24839 (2014).
[Crossref]

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25, 924–934 (2006).
[Crossref]

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” (2005).

Hsieh, J.

J. Hsieh, Computed Tomography: Principles, Design, Artifacts, and Recent Advances (SPIE, 2003), Vol. 114.

Hughes, K.

J. Burke, B. Deissler, K. Hughes, and C. Sackett, “Confinement effects in a guided-wave atom interferometer with millimeter-scale arm separation,” Phys. Rev. A 78, 023619 (2008).
[Crossref]

Ihrke, I.

L. Mignard-Debise and I. Ihrke, “Light-field microscopy with a consumer light-field camera,” in International Conference on 3D Vision (3DV) (IEEE, 2015), pp. 335–343.

Johnson, D. M.

S. M. Dickerson, J. M. Hogan, A. Sugarbaker, D. M. Johnson, and M. A. Kasevich, “Multiaxis inertial sensing with long-time point source atom interferometry,” Phys. Rev. Lett. 111, 083001 (2013).
[Crossref]

Kasevich, M.

Kasevich, M. A.

S. M. Dickerson, J. M. Hogan, A. Sugarbaker, D. M. Johnson, and M. A. Kasevich, “Multiaxis inertial sensing with long-time point source atom interferometry,” Phys. Rev. Lett. 111, 083001 (2013).
[Crossref]

Levoy, M.

Li, X.

K. D. Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nat. Phys. 3, 556–560 (2007).
[Crossref]

Lippmann, G.

G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. Theor. Appl. 7, 821–825 (1908).
[Crossref]

Mignard-Debise, L.

L. Mignard-Debise and I. Ihrke, “Light-field microscopy with a consumer light-field camera,” in International Conference on 3D Vision (3DV) (IEEE, 2015), pp. 335–343.

Nelson, K. D.

K. D. Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nat. Phys. 3, 556–560 (2007).
[Crossref]

Ng, R.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25, 924–934 (2006).
[Crossref]

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” (2005).

Sackett, C.

J. Burke, B. Deissler, K. Hughes, and C. Sackett, “Confinement effects in a guided-wave atom interferometer with millimeter-scale arm separation,” Phys. Rev. A 78, 023619 (2008).
[Crossref]

Sakmann, K.

Sugarbaker, A.

S. M. Dickerson, J. M. Hogan, A. Sugarbaker, D. M. Johnson, and M. A. Kasevich, “Multiaxis inertial sensing with long-time point source atom interferometry,” Phys. Rev. Lett. 111, 083001 (2013).
[Crossref]

Wang, J. Y. A.

E. H. Adelson and J. Y. A. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992).
[Crossref]

Weiss, D. S.

K. D. Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nat. Phys. 3, 556–560 (2007).
[Crossref]

Yang, S.

ACM Trans. Graph. (1)

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25, 924–934 (2006).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

E. H. Adelson and J. Y. A. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992).
[Crossref]

J. Phys. Theor. Appl. (1)

G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. Theor. Appl. 7, 821–825 (1908).
[Crossref]

Nat. Phys. (1)

K. D. Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nat. Phys. 3, 556–560 (2007).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (1)

J. Burke, B. Deissler, K. Hughes, and C. Sackett, “Confinement effects in a guided-wave atom interferometer with millimeter-scale arm separation,” Phys. Rev. A 78, 023619 (2008).
[Crossref]

Phys. Rev. Lett. (1)

S. M. Dickerson, J. M. Hogan, A. Sugarbaker, D. M. Johnson, and M. A. Kasevich, “Multiaxis inertial sensing with long-time point source atom interferometry,” Phys. Rev. Lett. 111, 083001 (2013).
[Crossref]

Other (5)

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” (2005).

L. Mignard-Debise and I. Ihrke, “Light-field microscopy with a consumer light-field camera,” in International Conference on 3D Vision (3DV) (IEEE, 2015), pp. 335–343.

M. Gu, Advanced Optical Imaging Theory (Springer, 2000), Vol. 75.

S. R. Deans, The Radon Transform and Some of Its Applications (Courier Corporation, 2007).

J. Hsieh, Computed Tomography: Principles, Design, Artifacts, and Recent Advances (SPIE, 2003), Vol. 114.

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Figures (8)

Fig. 1.
Fig. 1. Diagram of the optical layout of the light field microscope made for this experiment. The 4f optical system is simply the microscope objective and tube lens with focal lengths of f o and f tl , respectively. The system images onto the micro lens array, and the camera sensor is one micro lens focal length behind the micro lens array f ml .
Fig. 2.
Fig. 2. The sensor is a standard array of pixels represented here as a grid. The micro lenses (thick circles) are tiled across the surface in front of the sensor (as shown in Fig. 1) in a hexagon pattern and determine the ( s , t ) spatial positions. The pixels behind a given micro lens determine the ( u , v ) angular positions and are repeated for each micro lens.
Fig. 3.
Fig. 3. Geometric relation between the different coordinates used in calculating the point spread function. This represents only the microscope objective and tube lens portions of the optical system shown in Fig. 1. Here the coordinates are given, where the ( x , y ) plane is the object plane, and the ( x 3 , y 3 ) plane is the image plane, which corresponds to the MLA in Fig. 1.
Fig. 4.
Fig. 4. Diagram of the magneto optical trap and representation of the light field and reference camera orientations. The main image shows a top-down view of the vacuum chamber, and corresponding lasers and optics needed to create the MOT. The lower beam is actually coming down from off of the page through the vacuum chamber, and the reference camera is also off of the page looking down at approximately 53°. The inset image looks down the optical axis of the light field camera and shows how the reference camera is positioned. The coordinate vectors match the light field camera’s reference frame in both images. This is the same reference frame used in the images.
Fig. 5.
Fig. 5. This is the raw sensor data after cropping and the background has been subtracted. It is the sensor’s measurement of the light field. When looked at as a whole, the micro lenses are small enough to appear as individual pixels. The inset is a close up of the sensor and highlights the pattern produced on the sensor by the micro lens array, as diagrammed in Fig. 2.
Fig. 6.
Fig. 6. Contour surface through the normalized deconvolved volume at 0.44 voxel intensity produced from the light field data in Fig. 5. The elongation effect is noticeable and is why part of one of the clouds extends out of the volume.
Fig. 7.
Fig. 7. Left image is the projected image created from doing a Radon transform on each z slice in the reconstructed volume at the angle of the reference image. The right image is the reference image taken at an orthogonal view to the light field camera. Both have been scaled and plotted over the same range for comparison.
Fig. 8.
Fig. 8. There are two major areas where reconstruction artifacts affect the projection image data. The first is z -axis positions near the focal plane ( z = 0 ). As discussed in the text, this creates increases in intensity. The second is edge effects; near the z -axis edges of the volume, the intensity tends to increase. This is two z -axis slices through the data from MOT One chosen to give an example of the effect.

Tables (3)

Tables Icon

Table 1. Optical System Values

Tables Icon

Table 2. Calculated Relative Separation of the Two Peaks in the Projected Image and Reference Image

Tables Icon

Table 3. Calculated Lengths of the Peaks Along the Optical Axis and Back-Projection-Based Estimations of the Optical Axis Lengths Given the Minor Axis of an Ellipse Fit to the FWHM Data of the Standard On-Axis Image of the Atoms

Equations (10)

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R obj = 0.47 λ NA M ,
N u = D ml R obj ,
FDOF ( 2 + N u 2 ) λ n 2 NA 2 ,
ν ( z ) = D ml 0.94 λ M | z | ,
f = H g .
NA = n sin ( α o ) = M n sin ( α i ) ,
v 2 π λ r 3 sin ( α i ) ,
u 8 π λ z 3 sin 2 ( α i 2 ) ,
U 3 ( v , u ) = exp ( i u 4 sin 2 ( α i / 2 ) ) M d 1 2 λ 2 exp [ i v 2 4 N ( 1 + 1 / M ) ] 0 1 P ( ρ ) exp ( i u 2 ρ 2 ) J 0 ( ρ v ) 2 π d ρ ,
g ( k + 1 ) = diag ( H T 1 ) 1 diag ( H T diag ( H g ( k ) + b ) 1 f ) g ( k ) ,

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