## Abstract

We present a new imaging method to record multicolor digital holograms from objects emitting fluorescent light. The fluorescent light specific to the emission wavelength of various fluorescent dyes after excitation of three dimensional (3D) objects is recorded on a digital monochrome camera after reflection from a diffractive optical element (DOE). For each wavelength of fluorescent emission, the camera sequentially records three holograms reflected from the DOE, each with a different phase factor of the DOE’s function. The three holograms are superposed in a computer to create a complex valued Fresnel hologram of each fluorescent emission. The holograms for each fluorescent color are further combined in a computer to produce a multicolored fluorescence hologram and 3D color image.

©2007 Optical Society of America

## 1. Introduction

Fluorescence is one of the most widely used techniques in many areas of biology, material science and medical imaging because of its sensitivity, selectivity, low background and high contrast. Integration of holography into fluorescence three dimensional (3D) imaging has been difficult because holography requires coherent light and fluorescence emissions are incoherent. Non-fluorescent holography is a well established technique in which holograms are recorded by interfering two mutually coherent beams [1]. This technique cannot be applied to the incoherent light which is characteristic of the emitted light in a fluorescent object. Until now, scanning fluorescence holography [2–4], has been the only way to capture and create a hologram of the incoherent fluorescent emission from the emitted fluorescent light in 3D structures of an object. In scanning holography, a Fresnel Zone Plate (FZP) pattern from a coherent fluorescence excitation source scans the fluorescent labeled object such that at each and every scanning position the emitted light intensity is integrated by a detector. Since the mechanical scanning process is relatively slow, sensitive to vibration, requires a complex and expensive optical setup to create a FZP from the interference of two coherent beams, we believe it is advantageous to propose an alternative simpler method for fluorescence holography which is free of these drawbacks and has the promise of better performance.

Recently, we have proposed a new method of incoherent digital holography [5] coined FINCH as an acronym for Fresnel INcoherent Correlation Holography. By this method, light is reflected from a 3D object, propagates through or is reflected from a diffractive optical element (DOE) and is recorded by a digital camera. Each beam which originates from any object point is split into two different, mutually coherent, spherical waves. The beam splitting is done by the DOE grating, which operates as if it was a composition of two different diffractive spherical lenses. Therefore, the single wave-front originated from a point-source is divided by the DOE to two wave-fronts with different quadratic curves that propagate in the same direction. The intensity of the two wave-front interference, originated from the same point source, is accumulated incoherently on the camera pixel array with the other interferences from the entire object points to yield the complete hologram. In order to get rid of the twin image and the bias beam resulting from each single hologram which will be described later, three incoherent holograms are recorded sequentially, each with a different phase factor of the DOE. Using the common routines of digital holography [4–6], the three holograms are superposed in the computer, such that the result is a complex valued Fresnel hologram. When this hologram is reconstructed in the computer, a single 3D image of the object appears in the digital reconstruction space. A double channel interferometer with continuous temporal variation of the phase differences between the interfering beams to record non-fluorescent incoherent holograms has been described [7]. This is in contrast to the much simpler motionless single channel FINCH system reported here which has been readily able to produce high quality 3D fluorescent images.

In this study we employ the FINCH technique for color fluorescence imaging. The
proposed system produces a color Fresnel hologram which reconstructs the 3D object
with its original fluorescent colors. The dice objects in our demonstration contain
several spots of two fluorescent dyes each with different emission wavelengths. The
objects are illuminated by an arc lamp source with a bandpass filter to illuminate
the specimen with incoherent light of about 50 nm bandwidth and which can also
excite fluorescence in each of the fluorescent dyes. Several digital holograms are
generated for each of the different fluorescent colors on the dice and for the dice
themselves. Each emission color is introduced into the recording system by
restricting the emission with a specific chromatic filter. For each wavelength of
the fluorescence emission and the reflected non-fluorescent light image of the
object, a different Fresnel number is applied to the DOE’s grating. For
each wavelength, three holograms are sequentially recorded, each with a different
phase factor of the DOE’s function, such that the overall number of
captured holograms for *M* colors plus the complete reflected
non-fluorescent image of the object is
3∙(*M*+1). Every three holograms of the same
wavelength are superposed in a certain way such that the result is a complex valued
Fresnel hologram of this wavelength. The digital reconstruction from each hologram
is added to the rest, yielding a complete color 3D image of the original object. To
the best of our knowledge, the demonstrated holograms are the first fluorescence
holograms recorded without scanning and the first fluorescence multiwavelength
emission color holograms ever recorded.

## 2. Principles of color FINCH

An incoherent blue light source with a bandwidth of 56 nm illuminates a 3D object as
is shown in Fig. 1. The object’s fluorescent emission light is
introduced into the system after passing through one of the chromatic filters
F_{2}. After passing through lens L_{1}, the beam is reflected
from a spatial light modulator (SLM) toward a demagnification setup of two lenses
L_{2} and L_{3}, which projects the holographic pattern onto a
CCD camera. To understand the operational principle, we analyzed the system by
following its response to an input object of a single infinitesimal point. Knowing
the system’s point spread function (PSF), enables one to analyze the
system operation for any general object. In the following analysis, the light is
considered as quasi-monochromatic. Such assumption is valid under the condition that
the maximal optical path difference between the interfering beams in the system is
smaller than the coherence length which is inversely proportional to the spectral
bandwidth of the light source. This condition is well maintained in our single
channel on-axis holographic system. A Fresnel hologram of a point object is obtained
when the two interfering beams are, for instance, plane and spherical beams.
Therefore, we choose the DOE’s reflection function
*R*(*x _{D}*,

*y*) displayed on the SLM to be of the form,

_{D}where *λ* is the central wavelength introduced to the
system. The constant term of ½ in Eq. (1) contributes the plane wave, and the quadratic phase term is
the paraxial approximation of the spherical wave. The angle
*θ* is the phase shift needed in order to get rid of the
twin image and the bias term.

The reflection function of the DOE given by Eq. (1) implies that the system’s outcome can be viewed
as a sum of two overlapping imaging systems. Finding the location of each image is a
key concept for understanding this holographic recorder. In one system,
let’s call it system A, the DOE is actually a converging diffractive lens
with a focal length of *a*, whereas in the other system (system B)
the DOE serves as a plane mirror. In system A, a point source located at a distance
*d _{s}*=

*f*

_{1}from the lens L

_{1}is imaged to an image point at a distance (

*a*-

*d*

_{2})(

*f*

_{3}/

*f*

_{2})

^{2}beyond the camera plane. In this last expression we use the well-known fact that the axial magnification of an ordinary imaging system is given by the relation M

_{A}=M

_{T}

^{2}= (

*d*/

_{o}*d*)

_{s}^{2}, where M

_{T}is the transverse magnification, and

*d*is the distance from the output aperture to the image. For any point at (0,0,

_{o}*z*) located a distance

_{s}*d*=

_{s}*f*

_{1}-

*z*from the lens L

_{s}_{1}, assuming that

*z*<<

_{s}*f*

_{1}, the distance

*d*is approximately,

_{o}$$\phantom{\rule{2.4em}{0ex}}=\left[{\left(\frac{{r}^{2}}{{f}_{1}\lambda N}\right)}^{2}{z}_{s}+\frac{{r}^{2}}{\lambda N}-{d}_{2}\right]{\left(\frac{{f}_{3}}{{f}_{2}}\right)}^{2},$$

where the overall axial magnification *M*¯* _{A}* is the product of magnifications of the two consecutive imaging systems,

*r*is the DOE’s radius and

*N*is the DOE’s Fresnel number given by

*N*=

*r*

^{2}/

*λa*.

In system B, assuming that
*d _{s}*≈

*f*

_{1}, the object point is obtained far beyond the camera plane at a distance that justifies approximating the location of the image point at infinity. Therefore, for a point at (

*x*,

_{s}*y*,

_{s}*z*), the intensity on the camera plane is the square magnitude of the complex amplitude sum of the spherical wave converging at the distance

_{s}*d*beyond the CCD plane, together with a plane wave, as follows,

_{o}where the overall transverse magnification is *M*¯* _{T}* =

*f*

_{3}

*a*/

*f*

_{2}

*f*

_{1}=

*f*

_{3}

*r*

^{2}/

*λNf*

_{2}

*f*

_{1}. For a 3D object with intensity distribution

*g*(

*x*,

_{s}*y*,

_{s}*z*), illuminated by a narrowband incoherent illumination, the intensity of the recorded hologram is an integral over the entire PSFs, given by Eq. (3), over all the object points, as follows

_{s}$$+\iiint g\left({x}_{s},{y}_{s},{z}_{s}\right)\mathrm{exp}\left\{\frac{-i\pi}{{\lambda d}_{o}\left({z}_{s}\right)}\left[{\left(x-{\stackrel{\u0305}{M}}_{{T}^{x}s}\right)}^{2}+{\left(y-{\stackrel{\u0305}{M}}_{{T}^{y}s}\right)}^{2}\right]-i\theta \right\}{\mathit{dx}}_{s}{\mathit{dy}}_{s}{\mathit{dz}}_{s}).$$

Besides a constant term *C*′, Eq. (4) contains two terms of correlation between an object and a
quadratic phase, *z _{s}*-dependent, function, which means
that the recorded hologram is indeed a Fresnel hologram. In order to remain with a
single correlation term out of the three terms given in Eq. (4), we follow the procedure of on-axis digital holography [4, 5]. Three holograms of the same object are recorded each of
which with a different phase constant

*θ*. The final hologram

*H*is a superposition according to the following,

_{F}$$\phantom{\rule{3.9em}{0ex}}+{H}_{3}\left(x,y,\left[\mathrm{exp}\left(-{i\theta}_{2}\right)-\mathrm{exp}\left(-{i\theta}_{1}\right)\right]\right)$$

$$\phantom{\rule{1.8em}{0ex}}=\iiint g\left({x}_{s},{y}_{s},{z}_{s}\right)\mathrm{exp}\left\{\frac{i\pi}{{\lambda d}_{o}\left({z}_{s}\right)}\left[{\left(x-{\overline{M}}_{{T}^{x}s}\right)}^{2}+{\left(y-{\overline{M}}_{{T}^{x}s}\right)}^{2}\right]\right\}{\mathit{dx}}_{s}{\mathit{dy}}_{s}{\mathit{dz}}_{s},$$

where *H _{k}* is the

*k*-th recorded hologram with the phase constant

*θ*and

_{k}*k*=1,2,3.

A 3D image can be digitally reconstructed from
*H _{F}*(

*x*,

*y*) by calculating the Fresnel propagation [8]. The reconstruction results of different chromatic holograms are composed together to a complete color figure. In order to get the same transverse and axial magnifications for all the wavelengths we change the Fresnel number of the DOE such that

*d*(

_{o}*z*), given by Eq. (2), remains the same for all recorded wavelengths. In other words, the Fresnel number of the (

_{s}*i*+1)-th wavelength

*λ*

_{i+1}is

*N*

_{i+1}=

*N*

_{i}*λ*/

_{i}*λ*

_{i+1}where

*N*is the Fresnel number of the

_{i}*i*-th wavelength

*λ*.

_{i}## 3. Experimental results

An experiment showing the recording of a color fluorescence hologram was carried out
on the system shown in Fig. 1. The SLM (Holoeye HEO 1080P) is phase-only, and as so,
the desired function given by Eq. (1) cannot be directly displayed on this SLM. Instead, as a good
approximation for Eq. (1), we chose to display the required quadratic phase function
on only half of the SLM pixels. The rest of the pixels were modulated with a
constant phase, where the pixels of both types were selected randomly^{5}.
The small tilt angle of the SLM, from being orthogonal to the optical axis, does not
seemingly influence the results. The central 1024×1024 pixels of the SLM,
on an area of 9.7mm×9.7mm, were used for displaying the DOE. The phase
constants of
*θ*
_{1,2,3}=0°,120°,240°
were introduced into the three quadratic phase functions. The other specifications
of the system
are:*f*
_{1}=250mm,*f*
_{2}=150mm,
*f*
_{3}=35mm, *d*
_{1}=135mm,
*d*
_{2}=206mm.

A pair of 8mm×8mm dice (in which some of the dots were painted with either
red or green fluorescent paint) were positioned at the vicinity of the rear focal
point of lens L_{1}. The center of the die with red fluorescent spots and
the die with green fluorescent spots were at a distance of 228mm and 260mm from
L_{1}, respectevely. These dice were illuminated with a mercury arc lamp
(Zeiss-AttoArc 2, HBO 100W) in which only light with a peak wavelength of 472 nm and
a full width at half maximum (FWHM) bandwidth of 56 nm was allowed to pass through
bandpass filter F_{1}. All of the holograms were recorded by a cooled CCD
camera (Hamamatsu Digital Camera C4742-95, 12 bit, 1024×1280 pixels, bin
1) and processed by a PC. The first three holograms (0, 120 and 240 degrees) of the
non-fluorescent surfaces on the dice were recorded with an identical filter as the
source’s filter mentioned above placed in the emission filter slider
F_{2}. The Fresnel number for these holograms was chosen to be
*N _{B}*=10 (based upon a center wavelength of 472
nm). The magnitude and phase of the final complex hologram, superposed from the
first three holograms, are shown in Figs. 2(a) and 2(b), respectively. The reconstruction from the final
hologram was calculated using the Fresnel propagation formula [8]. The results are shown at the plane of the front face of the
front die in Fig. 2(c), and at the plane of the front face of the rear die
in Fig. 2(d). Note that in each plane a different die face is in
focus as is indeed expected from a holographic reconstruction of an object with a
volume. The second set of three holograms was recorded via a red filter in the
emission filter slider F

_{2}which passed fluorescent light with a peak wavelength of 626 nm and FWHM bandwidth of 11 nm. The Fresnel number during the recording of the ’red’ holograms was

*N*=7.8. The magnitude and phase of the final complex hologram, superposed from the ‘red’ set, are shown in Figs. 2(e) and 2(f), respectively. The reconstruction results from this final hologram are shown in Figs. 2(g) and 2(h) at the same planes as in Figs. 2(c) and 2(d), respectively. Finally, an additional set of three holograms was recorded with a green filter in emission filter slider F2 which passed fluorescent light with a peak wavelength of 516 nm and FWHM bandwidth of 16 nm. The Fresnel number during the recording of the ’green’ holograms was

_{R}*N*=9.2. The magnitude and phase of the final complex hologram, superposed from the ’green’ set, are shown in Figs. 2(i) and 2(j), respectively. The reconstruction results from this final hologram are shown in Figs. 2(k) and 2(l) at the same planes as in Figs. 2 (c) and 2(d), respectively. Compositions of Figs. 2(c), 2(g) and 2(k) and Figs. 2(d), 2(h) and 2(l) are depicted in Figs. 2(m) and 2(n), respectively. Note that all the colors in Fig. 2 are pseudo-colors. These last results yield a complete color 3D holographic image of the object including the red and green fluorescence. While the optical arrangement in this demonstration has not been optimized for maximum resolution, it is important to recognize that even with this simple optical arrangement, the resolution is good enough to image the fluorescent emissions with good fidelity and to obtain good reflected light images of the dice. Furthermore, in the reflected light images in Figs. 2(c) and 2(m) the system has been able to detect a specular reflection of the illumination from the upper right corner of the front dice.

_{G}## 4. Conclusions

In conclusion, we have proposed and demonstrated a process of recording color holograms of 3D fluorescent objects. This motionless system does not require complicated alignment or a laser and the bandwidth can be wider than conventional incoherent interferometers, entirely because this holographic recorder is implemented on a single channel setup. The proposed design might play an important role in many types of 3D fluorescence applications including fluorescence microscopy so that multicolor 3D structures and dynamic processes could be imaged without any scanning, and therefore would be expected to be faster then other methods.

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