## Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy |

Optics Express, Vol. 19, Issue 6, pp. 5047-5062 (2011)

http://dx.doi.org/10.1364/OE.19.005047

Acrobat PDF (1763 KB)

### Abstract

Fresnel Incoherent Correlation Holography (FINCH) enables holograms and 3D images to be created from incoherent light with just a camera and spatial light modulator (SLM). We previously described its application to microscopic incoherent fluorescence wherein one complex hologram contains all the 3D information in the microscope field, obviating the need for scanning or serial sectioning. We now report experiments which have led to the optimal optical, electro-optic, and computational conditions necessary to produce holograms which yield high quality 3D images from fluorescent microscopic specimens. An important improvement from our previous FINCH configurations capitalizes on the polarization sensitivity of the SLM so that the same SLM pixels which create the spherical wave simulating the microscope tube lens, also pass the plane waves from the infinity corrected microscope objective, so that interference between the two wave types at the camera creates a hologram. This advance dramatically improves the resolution of the FINCH system. Results from imaging a fluorescent USAF pattern and a pollen grain slide reveal resolution which approaches the Rayleigh limit by this simple method for 3D fluorescent microscopic imaging.

© 2011 OSA

## 1. Introduction

1. B. W. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, Y. Suzuki, and M. H. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. **22**(19), 1506–1508 (1997). [CrossRef]

2. J. Rosen and G. Brooker, “Non-Scanning Motionless Fluorescence Three-Dimensional Holographic Microscopy,” Nat. Photonics **2**(3), 190–195 (2008). [CrossRef]

3. O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip **10**(11), 1417–1428 (2010). [CrossRef] [PubMed]

1. B. W. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, Y. Suzuki, and M. H. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. **22**(19), 1506–1508 (1997). [CrossRef]

2. J. Rosen and G. Brooker, “Non-Scanning Motionless Fluorescence Three-Dimensional Holographic Microscopy,” Nat. Photonics **2**(3), 190–195 (2008). [CrossRef]

4. E. Y. Lam, X. Zhang, H. Vo, T.-C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt. **48**(34), H113–H119 (2009). [CrossRef] [PubMed]

5. G. Indebetouw, Y. Tada, J. Rosen, and G. Brooker, “Scanning holographic microscopy with resolution exceeding the Rayleigh limit of the objective by superposition of off-axis holograms,” Appl. Opt. **46**(6), 993–1000 (2007). [CrossRef] [PubMed]

3. O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip **10**(11), 1417–1428 (2010). [CrossRef] [PubMed]

6. J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. **32**(8), 912–914 (2007). [CrossRef] [PubMed]

7. J. Rosen and G. Brooker, “Fluorescence incoherent color holography,” Opt. Express **15**(5), 2244–2250 (2007). [CrossRef] [PubMed]

2. J. Rosen and G. Brooker, “Non-Scanning Motionless Fluorescence Three-Dimensional Holographic Microscopy,” Nat. Photonics **2**(3), 190–195 (2008). [CrossRef]

## 2. Materials and methods

### 2.1 Microscope and optical setup

**×**20 - 0.75 NA objective. In the majority of the experiments, the test subject was a negative USAF test slide (Edmund Optics 59204) which rested on a fluorescent plastic backing slide (Chroma) so that the clear features were fluorescent. We also imaged Mixed Pollen Grains (Carolina Biological 30-4264). Either a GFP or Cy3 filter set (Semrock) was used. The correct working distance between the objective and specimen was quite critical and established by first bringing the sample into focus by viewing the specimen through the microscope binoculars. Once the correct focus was established, it was kept constant, the tube lens and binocular were removed and the holography configuration shown in Fig. 1 was established. Because the SLM functions as the tube lens of the microscope, creating the spherical wave along with passing the plane wave to the camera, the current configuration contains a non-polarizing beam splitting cube so that the SLM is optically on axis to eliminate any possibility of image distortion from the SLM lens pattern. In our previous configuration of the microscope for FINCH holography, which we called FINCHSCOPE [2

**2**(3), 190–195 (2008). [CrossRef]

**×**2,048 pixel 12-bit CCD sensor) was varied between 164.5 mm and 800 mm. with the optimal distance

*z*(see Fig. 5 ) being 400 mm.

_{h}### 2.2 Spatial light modulator configuration, Fresnel patterns and polarizers

*f*is the focal length of the diffractive lens displayed on the SLM. Figure 3 demonstrates the functionality of the SLM as a diffractive spherical lens under illumination of two different laser beams with two wavelengths. Equating the argument of the lens transfer function for full aperture of the SLM to the argument of the digital phase pattern and isolating the focal length yields the following equation for the focal length,where Δ is the pixel size,

_{d}*N*is the number of pixels along the largest dimension of the SLM and

*x*

_{max}is the value of the matrix (

*x,y*) at the points ( ±

*N*/2,0) (for the experiments reported here, Δ = 8

*μm*,

*N =*1920 and

*x*

_{max}= 0.873). Substituting the SLM parameters into Eq. (1) gives the equations

*λ*= 532 nm and 633 nm, respectively. This is a difference between the calculated and experimental data in the slopes of the graphs in Fig. 3 of about 12.5% and 11% for

*λ*= 532 nm and 633 nm, respectively. The reflective SLM devoid of any pattern has a slight curvature for which we measured a focal length of

*f*= 8.2 meters. Taking this into account, the total measured focal length

_{SLM}*f*is calculated as the focal length of two successive lenses:where

_{m}*c*is the slope of the linear curve

*f*>>

_{SLM}*f*it can be approximated to a linear curve with an average slope

_{d,max}*c*ofwhere

_{a}*F*is the middle value of the range of 1

_{L,mid}*/F*, which in the present experiment is equal to

_{L}*F*≈244. Substituting the parameters

_{L,mid}*f*

_{SLM}= 8.2m,

*F*= 244,

_{L,mid}*c*(

*λ*= 532 nm) = 145473 and

*c*(

*λ*= 633 nm) = 122262 into Eq. (3) gives modified values for the slopes of

*c*(

_{a}*λ*= 532 nm) = 126421 and

*c*(

_{a}*λ*= 633 nm) = 108586. After accounting for the inherent curvature of the SLM, the difference between the calculated and experimental data in the slopes of the graphs in Fig. 3 is only 0.83% and 0.46% for

*λ*= 532 nm and 633 nm, respectively, which is within measurement error.

**×**1920 pixels). The

*z*distance used (400 mm) for the images reported here was greater than the 230 mm calculated minimum focal length of the SLM. The minimum focal length is determined by the SLM's pixel size Δ (8 microns), and the number of pixels

_{h}*N*(1920) along the SLM's diameter, according to the inequality

*f*≥

_{d}*N*Δ

^{2}/

*λ*The SLM firmware was modified and confirmed to produce the desired focal lengths and phase shifts (using 532 nm and 633 nm coherent collimated and expanded laser beams for calibration and testing) to deliver a full 2π phase shift over its working range of 256 gray levels. Diffractive lenses such as the lens patterns on this SLM will have multiple higher diffraction order foci in the desired focal plane, as well as other, undesired, focal planes at different focal distances than the desired focal plane. In the configuration used here, the focusing efficiency of the SLM into the central image of the desired focal plane was measured to be greater than 50%, with insignificant intensity concentrated in undesired planes of focus. Furthermore, at the camera-SLM distance of 400 mm, the higher diffraction order images in the desired focal plane did not project onto the CCD. Recently an excellent review [9

9. C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. **5**(1), 81–101 (2011). [CrossRef]

### 2.3 Computational methods

*θ*

_{k}_{= 1,2,3}= 0, 120 and 240 degrees [2

**2**(3), 190–195 (2008). [CrossRef]

## 3. Theoretical considerations

*z*before the objective, where

_{s}*ϕ*

_{1}angle to the

*x*axis,

*f*is the focal length of the objective,

_{o}*d*

_{1}is the distance between the objective and the SLM and

*A*are the constant amplitudes in the

_{x}, A_{y}*x, y*axes, respectively. The asterisk denotes a two dimensional convolution and are unit vectors in the

*x, y*directions, respectively. For the sake of shortening, the quadratic phase function is designated by the function

*Q*, such that

*L*stands for a the linear phase function, such that,

*x*. The light polarized in

*y*direction is reflected from the SLM with only a constant phase shift. Therefore the complex amplitude on the output plane of the SLM is,where

*B*and

_{Q}*B*are complex constants.

_{M}*θ*is one of the three angles used in the phase shift procedure in order to eliminate the bias term and the twin image [6

6. J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. **32**(8), 912–914 (2007). [CrossRef] [PubMed]

7. J. Rosen and G. Brooker, “Fluorescence incoherent color holography,” Opt. Express **15**(5), 2244–2250 (2007). [CrossRef] [PubMed]

*ϕ*

_{2}to the

*x*axis, has linear polarization in the direction of the polarizer axis. Therefore we can abandon the vector notation and express the complex amplitude beyond the second polarizer, on the CCD plane, aswhere

*z*is the distance between the SLM and the CCD. The intensity of the recorded hologram is,

_{h}*A*,

_{o}*C*

_{2},

*C*

_{3}are constants and

*I*(

_{p}*x*

_{2},

*y*

_{2}) is the PSF of the recording part of the FINCH. To avoid the problem of the twin image, one of the interference terms, (the second or third terms) in Eq. (8) should be isolated by the phase-shifting procedure [10

10. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. **22**(16), 1268–1270 (1997). [CrossRef] [PubMed]

11. B. Katz, D. Wulich, and J. Rosen, “Optimal noise suppression in Fresnel incoherent correlation holography (FINCH) configured for maximum imaging resolution,” Appl. Opt. **49**(30), 5757–5763 (2010). [CrossRef] [PubMed]

*z*from the hologram given by Eq. (9), and at a transverse location

_{r}*ϕ*

_{1}and

*ϕ*

_{2}are chosen in order to maximize the interference terms [the second and third terms in Eq. (8)]. Their precise values depend on the values of the constants |

*B*| and |

_{Q}*B*|. In this study we choose their values empirically by picking the angles that yield the best reconstructed image.

_{M}*z*, as was indeed chosen in the present experiment. In this case

_{s}= f_{o}*f*→∞, and therefore

_{e}*f*

_{1}

*= -f*,

_{d}*z*(

_{r}= ±*z*) and

_{h}-f_{d}*D*are the diameters of the SLM, and the recorded hologram, respectively.

_{H}*NA*and

_{in}*NA*are the numerical apertures of the system input and output, respectively. The

_{out}*NA*is independently determined by the objective and cannot be changed by the design of the FINCH system. However the product

_{in}*NA*is dependent on the system parameters and our goal should be to keep this product equal or larger than

_{out}M_{T}*NA*in order not to reduce the resolution determined by the input aperture. Therefore, referring to Eq. (12), an optimal FINCH system satisfies the inequality,In this inequality all the parameters are well defined besides the diameter of the hologram. This size is dependent on the overall size of the reconstructed image. Based on simple geometrical considerations the diameter of the hologram is,where

_{in}*a*is the ratio between the image and the SLM sizes.

*a*ranges between almost zero for an image of a point, to 1 for a full frame image. Substituting Eq. (14) and quantities

*z*|

_{r}=*f*| and

_{d}-z_{h}*f*. Therefore by calculating the inequality in Eq. (13) we find the optimal

_{d}*f*in sense of best image resolution. The solution of Eq. (15) is

_{d}11. B. Katz, D. Wulich, and J. Rosen, “Optimal noise suppression in Fresnel incoherent correlation holography (FINCH) configured for maximum imaging resolution,” Appl. Opt. **49**(30), 5757–5763 (2010). [CrossRef] [PubMed]

*a =*1. Consequently the focal length of the diffractive lens should be equal or smaller than twice the distance between the SLM and the CCD, or in a formal way,

*f*= 2

_{d}*z*is the optimal choice for the length of the focal length of the diffractive lens.

_{h}## 4. Results

*x*axis.

## 5. Discussion

12. G. D. Love, “Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator,” Appl. Opt. **36**(7), 1517–1520 (1997). [CrossRef] [PubMed]

*ϕ*

_{1}:

*ϕ*

_{2}(i.e. from (0,0) to (90,90)). The hologram in Fig. 8 at (0,0) is composed mostly of spherical wave from the SLM, while the hologram at (90,90) is composed mostly of plane wave. The corresponding reconstructed images in Fig. 9 both have extremely poor resolution, even though the holograms from which they are reconstructed are the brightest. The highest resolution reconstructed images in Fig. 9 derive from the holograms taken with the polarizers at intermediate angles, transmitting approximately equal amounts of plane and spherical wave. In contrast to what would be expected in conventional imaging, the highest resolution reconstructed images did not come from the holograms with the highest intensity, but rather from the holograms in which the greatest proportion of both plane and spherical waves produced the interference pattern. Thus, in FINCH imaging, obtaining a high degree of interference visibility between the couples of plane and spherical waves is a more critical factor than simply maximizing the intensity of the recorded holograms.

*f*of an imaging lens leads to a change of the image distance do according to the imaging formula 1/

*d*+ 1/

_{i}*d*= 1/

_{o}*f*, where

*d*is the distance of object from the imaging lens. Therefore the transverse magnification

_{i}*M*is also sensitive to the change of the focal length because of the relation

_{T}*M*=

_{T}*d*/

_{o}*d*. Consequently, for each wavelength there is a different image at a different location and with a different scale, which results in blurring of the overall image. This is not the case when the image being recorded is a FINCH hologram. As derived above from Eqs. (9) and (10), and for the case that

_{i}*z*,

_{s}= f_{o}*f*→∞, we see that

_{e}*f*

_{1}

*= -f*,

_{d}*z*(

_{r}= ±*z*) and

_{h}-f_{d}*z*is sensitive to λ because of the dependence of

_{r}*f*with λ. However the transverse magnification

_{d}*M*is independent of

_{T}*f*and therefore it is independent of λ. In other words, there is a different image for each wavelength, as in the case of regular imaging, but all the images appear in the same scale with FINCH imaging and are thus superimposed so that no blurring occurs due to chromatic diffraction effects.

_{d}## Acknowledgements

## References and links

1. | B. W. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, Y. Suzuki, and M. H. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. |

2. | J. Rosen and G. Brooker, “Non-Scanning Motionless Fluorescence Three-Dimensional Holographic Microscopy,” Nat. Photonics |

3. | O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip |

4. | E. Y. Lam, X. Zhang, H. Vo, T.-C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt. |

5. | G. Indebetouw, Y. Tada, J. Rosen, and G. Brooker, “Scanning holographic microscopy with resolution exceeding the Rayleigh limit of the objective by superposition of off-axis holograms,” Appl. Opt. |

6. | J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. |

7. | J. Rosen and G. Brooker, “Fluorescence incoherent color holography,” Opt. Express |

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

9. | C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. |

10. | I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. |

11. | B. Katz, D. Wulich, and J. Rosen, “Optimal noise suppression in Fresnel incoherent correlation holography (FINCH) configured for maximum imaging resolution,” Appl. Opt. |

12. | G. D. Love, “Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator,” Appl. Opt. |

**OCIS Codes**

(050.1950) Diffraction and gratings : Diffraction gratings

(090.1760) Holography : Computer holography

(090.1970) Holography : Diffractive optics

(090.2880) Holography : Holographic interferometry

(100.6890) Image processing : Three-dimensional image processing

(110.0180) Imaging systems : Microscopy

(110.6880) Imaging systems : Three-dimensional image acquisition

(120.5060) Instrumentation, measurement, and metrology : Phase modulation

(180.2520) Microscopy : Fluorescence microscopy

(180.6900) Microscopy : Three-dimensional microscopy

(260.2510) Physical optics : Fluorescence

(330.1720) Vision, color, and visual optics : Color vision

(090.1995) Holography : Digital holography

**ToC Category:**

Microscopy

**History**

Original Manuscript: December 13, 2010

Revised Manuscript: February 22, 2011

Manuscript Accepted: February 27, 2011

Published: March 2, 2011

**Virtual Issues**

Vol. 6, Iss. 4 *Virtual Journal for Biomedical Optics*

**Citation**

Gary Brooker, Nisan Siegel, Victor Wang, and Joseph Rosen, "Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy," Opt. Express **19**, 5047-5062 (2011)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-6-5047

Sort: Year | Journal | Reset

### References

- B. W. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, Y. Suzuki, and M. H. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22(19), 1506–1508 (1997). [CrossRef]
- J. Rosen and G. Brooker, “Non-Scanning Motionless Fluorescence Three-Dimensional Holographic Microscopy,” Nat. Photonics 2(3), 190–195 (2008). [CrossRef]
- O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10(11), 1417–1428 (2010). [CrossRef] [PubMed]
- E. Y. Lam, X. Zhang, H. Vo, T.-C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt. 48(34), H113–H119 (2009). [CrossRef] [PubMed]
- G. Indebetouw, Y. Tada, J. Rosen, and G. Brooker, “Scanning holographic microscopy with resolution exceeding the Rayleigh limit of the objective by superposition of off-axis holograms,” Appl. Opt. 46(6), 993–1000 (2007). [CrossRef] [PubMed]
- J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32(8), 912–914 (2007). [CrossRef] [PubMed]
- J. Rosen and G. Brooker, “Fluorescence incoherent color holography,” Opt. Express 15(5), 2244–2250 (2007). [CrossRef] [PubMed]
- J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
- C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5(1), 81–101 (2011). [CrossRef]
- I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997). [CrossRef] [PubMed]
- B. Katz, D. Wulich, and J. Rosen, “Optimal noise suppression in Fresnel incoherent correlation holography (FINCH) configured for maximum imaging resolution,” Appl. Opt. 49(30), 5757–5763 (2010). [CrossRef] [PubMed]
- G. D. Love, “Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator,” Appl. Opt. 36(7), 1517–1520 (1997). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.