WO2001023965A1

WO2001023965A1 - Digital interference holographic microscope and methods

Info

Publication number: WO2001023965A1
Application number: PCT/US2000/026462
Authority: WO
Inventors: Myung K. Kim
Original assignee: University Of South Florida Division Of Patents And Licencing
Priority date: 1999-09-27
Filing date: 2000-09-27
Publication date: 2001-04-05
Also published as: AU7718700A

Abstract

A simple digital holographic apparatus and method allow reconstruction of three-dimensional objects with a very narrow depth of focus or high axial resolution. A number or holograms are optically generated using different wavelengths spaced at regular intervals. They are recorded, such as on a digital camera, and are reconstructed numerically. Multiwavelength interference of the holograms results in contour planes of very small thickness and wide separation. Objects at different distances from the hologram plane are imaged clearly and independently with complete suppression of the out-of-focus images. The technique is uniquely available only in digital holography and has applications in holographic microscopy.

Description

DIGITAL INTERFERENCE HOLOGRAPHIC MICROSCOPE AND METHODS

BACKGROUND OF THE INVENTION

Cross-Reference to Related Application This application claims priority to provisional application 60/156,253, filed September

27, 1999.

Field of the Invention

The present invention relates to microscopic imaging, and, more particularly, to

holographic microscopy for reconstruction of three-dimensional objects and optical tomographic imaging for selectively imaging cross sections of an object.

Description of Related Art

Imaging of microscopic objects is an essential art, not only in biology and medicine,

but also in many other fields of science and technology, including materials science,

microelectronics engineering, and geology. Modern microscopy takes advantage of

discoveries on the interaction between electromagnetic and other fields with material objects,

and has taken on numerous incarnations, such as electron transmission and scanning

microscopes, the scanning tunneling microscope, the atomic force microscope, and the laser

scanning confocal microscope (Isenberg, 1998).

Rapid progress in electronic detection and control, digital imaging, image processing,

and numerical computation has been crucial in advancing modern microscopy. By equipping

an optical microscope with a digital or video camera, a range of image processing and pattern

recognition techniques can be applied for automated image acquisition and analysis (Herman

and Lemasters, 1993). One particular aspect of microscopic imaging of interest is the axial resolution or depth

of focus. In a conventional optical microscope, the lateral resolution can be a fraction of a

micrometer, whereas the axial resolution is typically several micrometers or more. This leads to two related difficulties: One is that the axial position cannot be determined with better than

a few-micrometer accuracy; another is that the overlap of images from object planes several

micrometers apart leads to blurring and degradation of images. Usually the only remedy

available is physical sectioning of the specimen into thin slices, which precludes a large range

of materials from being studied.

A remarkable solution to these problems was the scanning confocal microscope,

developed just over a decade ago (Sheppard and Shotton, 1997). by illumination of a single

object point and placement of a detection aperture at the image point, the detector behind the

aperture registers a light signal originating only from the object point. A two- or three-

dimensional image is constructed by pixel-by-pixel scanning of the object volume. The whole

of the resulting image is sharply in focus, and the size of the acquirable image is limited only

by the stability and speed of the scanning and processing system.

Another important optical scanning system is the near-field optical scanning

microscope, where the light signal is probed by a highly tapered optical fiber at a distance only

a fraction of an optical wavelength from the sample surface, thereby circumventing the

diffraction limit of resolution in far-field imaging. However, the application of this technique

in imaging wet and delicate biological samples has been limited because of the requirement

to maintain a constant surface-probe distance with accuracy and stability. It is more suitable

for the study of macromolecular structures, as with other related scanning devices that utilize

electron tunneling, atomic force, and other subtle interactions on the atomic and molecular

level. Holography was originally invented in an attempt to improve the resolution of a

microscope (Hariharan, 1996). Both the amplitude and phase information of the light wave

are recorded in a hologram by the interference of an object wave that is to be imaged with a reference wave of simple structure such as a plane or spherical wave. The interference pattern

is recorded in a variety of media, most commonly on a photographic plate. The object wave

is reconstructed as one of the diffraction patterns when a replica of the reference wave is

incident on the photographic plate. The resulting image is an exact copy of the light wave that

originally emanated from the object, and thus has the property of perspective vision.

Because the holographic image retains the phase as well as the amplitude information, a variety of interference experiments can be performed, and this is the basis of many

interferometric applications in metrology. It is possible accurately to measure deformation

and other variations of an object at a submicrometer level because of advances in digital

imaging and numerical computing technology. Thus it is often advantageous to replace steps

of the holographic procedure with digital processes (Yaraslavskii and Merzlyakov, 1980).

In computer-generated holograms (CGH) the interference pattern is computed from

a mathematical definition of a virtual object and reference (Trester, 1996). The patter is

output to a hard-copy device, and laser illumination results in an optical hologram image.

On the other hand, in computer-reconstructed holograms (CRH), the optical

interference pattern of a real object and reference is recorded using an electronic or digital

camera (Schnars and Jϋptner, 1996). The pattern is digitized and stored in a computer, and

the holographic image is recreated on the computer by numerical calculation.

In either CGH or CRH, the numerical calculation basically imitates the optical

diffraction process as the light wave propagates from the object to the hologram plane or from

the hologram plane to the image plane. This can be accomplished using Fresnel diffraction theory or Huygens wavelet theory (Kreis et al, 1997). An important aspect of research in this

area is in attempts to minimize the computational load using, for example, segmentation of

holograms and horizontal-only parallax (Karnaukhov et al., 1998; Yang et al., 1998a,b).

Digital holography alleviates the need for wet chemical processing of a photographic

plate, although at some expense of resolution. However, once the amplitude and phase (i.e., all the essential information) of the light wave are recorded numerically, one can easily subject

these data to a variety of manipulations, and so digital holography offers capabilities not

available in conventional holography. For example, the phase information of the light wave is available directly from the numerical reconstruction and greatly simplifies interferometric

deformation analysis (Seebacher et al., 1998; Kreis etal, 1998; Cuche et al, 1999; Brown and

Pryputniewicz, 1998).

Holography can be applied to microscopy in two alternative ways. In one, a hologram

of a microscopic object is taken directly, and the hologram is inspected using a microscope;

in the other, a microscope is used first to magnify the object image, and the hologram is taken

of that image. Holographic microscopy has been particularly useful in particle analysis, where

a particle count has to be obtained in a volume of fluid (Nikram, 1992). With a conventional

microscope, the constant motion of particles into and out of the focal plane makes it difficult

to ascertain an accurate count as the focal plane is scanned across the entire sample volume.

A holographic micrograph freezes the three-dimensional field, and a particle count can

proceed by focusing on successive planes.

Holographic microscopy in three-dimensional imaging applications has been limited

partly because of the inherent scale distortion of an optical microscope image of a volume

object. The axial magnification goes as the square of the lateral magnification, so that the two

directions magnify with different ratios, and the lateral magnification also depends on the axial distance. When the hologram is viewed by focusing on a plane, the same problem of

out-of-focus image blurring is present as in an optical microscope (Zhang and Yamaguchi,

1998; Poon et aL, 1995).

Application of digital holography in microscopy holds potentially attractive benefits (Schilling et al., 1997). In principle, once the amplitude and phase information of the object

image is numerically stored, it can be manipulated by image processing techniques for

removal of distortion and out-of-focus blurring, interference measurements can yield

subwavelength resolution of features, and particle analysis and feature recognition can be automated with greater efficiency.

Another imaging technique, tomography, has been utilized in biomedical and materials

sciences (Robb, 1997), with optical tomography most useful in microscopic imaging because

of the short wavelength and limited penetration depth of most biological surfaces. For

example, laser confocal microscopy (Sheppard and Shotton, 1997) uses aperturing of both the

illuminated sample volume and the detector aperture, thereby rej ecting all scattered light other

than from the focal volume. Optical coherence tomography (Huang et al., 1991 ; Morgner et

al., 2000) is a time-of-flight measurement technique, using ultrashort laser pulses or a

continuous-wave laser of very short coherence time. In both of these methods the signal is

detected one pixel at a time, and the three-dimensional image is reconstructed by scanning the

three-dimensions pixel by pixel. Although microsca ning using piezo actuators is an

important technique, being able to obtain image frames at a time would have technical

advantages.

By recording the phase as well as the intensity of light waves, holography allows

reconstruction of the image of 3D objects, and gives rise to many metrological and optical

processing techniques (Hariharan, 1996). It is now possible to replace portions of the holographic procedure with electronic processes (Yaroslavsky and Eden, 1996). For example,

in digital holography the hologram is imaged on a CCD array, replacing photographic plates of conventional holography. The digitally converted hologram is stored in a computer, and

its diffraction is numerically calculated to generate simulation of optical images.

With digital holography, real-time processing of the image is possible, and the phase

information of the reconstructed field is readily available in numerical form, greatly

simplifying metrological applications (Cuche et al., 1998). Previously limiting memory and speed factors have improved (Trester, 1996; Piestun et al., 1997). On the other hand, for the

purpose of tomographic imaging, although the hologram produces a 3D image of the optical

field, this does not by itself yield the tomographic distance information to the object surface

points, other than by focusing and defocusing of the object points, which is really a subjective

decision (Poon et al., 1995; Zhang and Yamaguchi, 1998a). The distance information can be

obtained in time-of-flight-type measurements, or it can be determined by counting the number

of wavelengths or some multiples of it, which is the basis of various interference techniques.

One technique is the interference of two holograms recorded at two different

wavelengths, resulting in a contour interferogram with the axial distance between the contour

planes inversely proportional to the differences in wavelengths. In digital holography, it is

possible to extend the process to recording and reconstruction of many holograms without introducing any wavelength mismatch or crosstalk. If a number of regularly spaced

wavelengths are used for recording and reconstruction, then the peaks of the cosine-squared

intensity variation of two-wavelength interference become sharper and narrower, as when a

number of cosines with regularly spaced frequencies are added. SUMMARY OF THE INVENTION

It is an object of the present invention to provide a simple digital holographic method

and apparatus for reconstructing three-dimensional objects with a very narrow depth of focus or axial resolution.

It is another obj ect to provide such a method and apparatus that affords submicrometer

resolution in both the lateral and the longitudinal directions.

It is a further object to provide such a method and apparatus wherein the blurring and

degrading of images due to out-of-focus object planes are substantially completely suppressed.

It is an additional object to provide such a method and apparatus that carries out an

interference process in numerical virtual space.

Another object is to provide such a method and apparatus wherein the obtained optical

sectioned images can be reassembled into a three-dimensional digital model that can be

further manipulated for specific applications, such as correction of scale distortion, arbitrary

section and cutaway views, and automatic feature enhancement and identification.

A further obj ect is to provide a method and apparatus for imaging a three-dimensional

object having a diffuse surface.

An additional object is to provide such a method and apparatus for generating a three-

dimensional numerical model of the imaged surface structure.

These and other objects are achieved by the present invention, a first embodiment of

which comprises an apparatus and method for imaging three-dimensional microscopic volume

objects with digital holographic microscopy.

As is known in the art, interference of two holograms recorded at two different

wavelengths results in a contour interferogram, with the axial distance between the contour

planes inversely proportional to the difference in wavelengths. In CRH, unlike in conventional holography, the reconstruction of each hologram is done using the corresponding

wavelength that was actually used in the recording process. Therefore, it is possible to extend

the process to recording and reconstruction of many holograms without introducing any wavelength mismatch. If a number of regularly spaced wavelengths are used for recording

and reconstruction, then the peaks of cosine-squared intensity variation of two-wavelength

interference becomes sharper and narrower, as when a number of cosines with regularly

spaced frequencies are added.

The present invention addresses a practical problem in microscopy, where the axial

magnification goes as the square of the transverse magnification. Even at moderate

magnification, it is difficult to bring the entire microscopic obj ect into focus, while the out-of-

focus portions of the object image contribute to blurring and noise of the focal plane image.

Confocal scanning microscopy (CSM) addresses this problem very successfully (Sheppard and

Shotton, 1997), although the requirement of stability and precision of lengthy mechanical

scanning can be quite significant.

A hologram has depth perception and axial resolution, but determination of axial

location in particle analysis, for example, depends only on the focusing of the image as the

depth is varied (Zhang and Yamaguchi, 1998b), and out-of-focus blurring presents the same

problem as in microscopy.

The present invention involves no mechanical motion, and wavelength scanning and

multiple exposure can be electronically automated for speed and stability. Furthermore, many

of the holographic interferometric and optical processing techniques can be applied to the

resulting images for various applications. The principle of wavefront reconstruction by holography is well known. The electric

field E₀ arriving from an object interferes with a planar, or other simply structured, write

reference wave E_r, resulting in an intensity pattern of:

I~ \ E + E_n \ ² = \ E I ² + | __. | ² + i_ ^*£. + __ __₀ ^*

which is recorded in some manner. In CRH one may subtract the zero-order terms j E_r | ² and I E₀1², and the remaining terms give rise to the holographic twin images. For simplicity, one

neglects the effect of the conjugate image and considers the third term in the above equation

only, and also lets the reference wave be planar and incident perpendicular to the hologram

plane, so that E_r - 1. In reconstruction, if one also uses E_r as the read reference wave, then

the diffracted wave is proportional to E₀, a replica of the original obj ect wave (or its conjugate E₀ ^*).

Now consider an object point P located at (x₀, ₀, z₀), which emits a Huygens spherical

wavelet proportional to A(P)exp(ikr_P) measured at an arbitrary point Q = (x, y, z), where r_P =

\r_P - r_Q\ is the distance between P and Q, and the 1/r dependence of the amplitude is

neglected. The wave propagates in the general z direction. The factor __(_P) represents the

field amplitude and phase at the object point. For an extended object, the field at Q is

proportional to the above wavelet field integrated over all the points on the object:

-, < _>> _ ³_r_ A ( P) exp ( ikr_p)

This is the field that is present in the vicinity of the object under monochromatic illumination,

and this is also the field reconstructed by holography. The factor exp(ikr_P) represents the

propagation and diffraction of the object wave. Now suppose a number of copies of the electric field are generated by varying the wave numbers k (or wavelengths λ), all other

conditions of object and illumination remaining the same. Then the resultant field at Q is:

E [ Q) ~ ∑ [ d³r_pA ( P) exp ( ikr_p)

-f d³r_pA ( P) ∑ exp ( ikr_p)

X ^>r_pA ( P) δ (ι:. A ( Q)

That is, for a large enough number of wave numbers k, the resultant field is proportional to

the field at the object, and nonzero only at object points. In practice, if one uses a finite

number N of wavelengths at regular intervals of Δλ (with corresponding intervals of

frequencies Af), then the object image A(P) repeats itself at axial distances A = λ²/Δλ = c/Af

with an axial resolution of δ = Λ/N. By using appropriate values of Δλ and N, the contour

plane distance A can be matched to the axial extent of the object and δ to the desired level of

axial resolution. Note that for a given level of axial resolution δ, the required range of

wavelengths NΔλ is the same as the spectral width of low-coherence or short-pulse lasers in

optical coherence tomography.

Optical sectioning microscopy by wavelength-scanning digital interference holography

(WS-DIH) proceeds as follows. A microscopic object is illuminated by a laser, and a

microscope lens forms a real magnified image of the object. Light from this intermediate

image and a reference beam interferes at a CCD array surface, which is recorded digitally into

a computer. The laser wavelength is stepped by Δλ for the next exposure, and the process is repeated N times, which completes the recording process. The axial scale of the object

determines the necessary wavelength step Δλ. Using the example of a 10-μm-radius sphere

and 50^χ lateral magnification, the longitudinal extent of the intermediate image is 20 μm x 50² = 50 mm, which sets the minimum for the contour plane distance A. Using 600-nm light,

the required frequency step is Δ = c Δλ/λ² = 6 GHz. To obtain effective axial resolution of,

say, 1 μm = 20 μm/20, one needs to take 20 hologram images while scanning the laser frequency up to 120 GHz = 4 cm^"1. These parameters are easily within range of many laser

systems, including dye lasers and semiconductor lasers. Note that the frequency step Δ is inversely proportional to the object axial scale A.

The set of N digitally stored holograms represents the complete information required for computational reconstruction of the three-dimensional image. For each hologram, after

subtraction of zero-order intensities, a diffraction theoretical formula is applied to compute

the light wave field of the image. Repeat the computation of N holographic images, and they

are added together for digital interference. The resultant image is an intensity distribution

pattern that corresponds to three-dimensional map of scattering centers of the obj ect, such as

the boundary surfaces, internal structures, and other points of irregularities in absorption or

dispersion of light.

The result can be displayed as two-dimensional cross sections of the object at an

arbitrary distance from the hologram plane. With the set of numerical representation of the

images, further manipulation and processing is possible. For example, the microscopic image

distortion, including the unequal lateral-axial magnifications and the axial dependence of the

lateral magnification, can be processed out by applying corrective scale factors. The corrected

cross sections can then be reassembled into a three-dimensional computer model with natural aspect ratios. The three-dimensional computer model is then available for application-specific

manipulations such as viewpoint changing, cutaway views, feature enhancement, and others.

The system of the present invention takes advantage of the unique power of digital

holography to provide a simple and versatile mode of three-dimensional microscope imaging.

One may put this concept in perspective in terms of its potential advantages over other

imaging modes and of possible difficulties that may arise.

• The lateral resolution should be as good as conventional optical microscopy, except

that the present system is a coherent imaging system, and so one needs to exercise care with speckle noise and other interference effects. On the other hand, the multiple

exposure of the scheme of the present invention tends to have a signal-averaging

effect. Studies seem to indicate such an enhancement of image quality.

• The axial or longitudinal resolution is excellent in comparison with conventional

optical microscopy. Scanning confocal microscopy was developed to address the

problem of axial resolution in conventional optical microscopy. The axial resolution

of a confocal system is determined mainly by the focal depth of the illuminated spot,

to ~ 0.5 μm. With WS-DIH, a comparable axial resolution may be expected or even

exceeded. Digital holography has been used to demonstrate ~ λ/10 or ~ 50 nm

vertical resolution in the inspection of a microelectronics circuit.

• The wavelength scanning system of the present invention has no mechanical moving

components. In principle, the amount of voxel (volume element) data generated by

WS-DIH is the same as in SCM: M_x * M_y * N, where the Ms are the number of pixels

in the x andy directions and N is the number of z sections. In SCM, the system has

to raster scan each plane pixel by pixel and then repeat the process for N planes. The requirement of mechanical accuracy and stability can be substantial and entails an elaborate feedback control system. On the other hand, the present system acquires a

single whole plane of data in one shot, and in most laser systems tuning and scanning

of the gigahertz range is electronically controllable, providing efficiency, stability, and accuracy. With present CCD technology, however, the bottleneck may occur at the

image transfer rate between the CCD array and the computer memory.

• The system of the present invention is a holographic system, and as such, the complete

amplitude and phase information of the light field is available. One can take advantage of this information that is not available in other imaging systems, for

applications in interferometry and holographic image processing.

The features that characterize the invention, both as to organization and method of

operation, together with further obj ects and advantages thereof, will be better understood from

the following description used in conjunction with the accompanying drawing. It is to be

expressly understood that the drawing is for the purpose of illustration and description and is

not intended as a definition of the limits of the invention. These and other objects attained,

and advantages offered, by the present invention will become more fully apparent as the

description that now follows is read in conjunction with the accompanying drawing.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of an apparatus for multiwavelength digital holography.

FIGS.2A-2E are reconstructions of an image of a single object (OBJ1) using a single

wavelength: FIG. 2 A, reference beam; FIG. 2B, object beam at the screen; FIG. 2C, interference between the reference and the obj ect; FIG.2D, intensity patterns of FIGS .2 A and

2B subtracted from FIG. 2C; FIG. 2E, numerically reconstructed image at z_i = z₀ = 149 cm.

FIGS. 3A-C are reconstructions of images of two objects (OBJ1 and OBJ2) using a

single wavelength: FIG.3A, interference pattern between reference and object, minus zero-

order terms; numerically reconstructed images: FIG. 3B, at z_ = z_0l = 149 cm; and FIG. 3C,

at Zj - z-₂ - 165 cm.

FIGS. 4A-4E are reconstructed image patterns as functions of image distance. The

horizontal axis is z in cm, and the vertical axis, in mm, is a slice of the reconstructed image

along the dotted line shown in FIG. 3C: FIG.4 A, a single wavelength or frequency; FIG.4B,

combination of two holograms at relative frequencies, 0.0 and 1.0 GHz; FIG.4C, two relative

frequencies, 0.0 and 2.0 GHz; FIG. 4D, three relative frequencies, 0.0, 1.0, and 2.0 GHz;

FIG. 4E, eleven relative frequencies, 0.0, 1.0, 2.0,..., 10.0 GHz.

FIGS.5A and 5B are reconstructed images with two objects using eleven holograms:

FIG. 5 A, at z = z_Λ = 149 cm; FIG. 5B, at z, = z_o2 = 165 cm.

FIG. 6 is a schematic of an apparatus for digital interference holography.

FIG. 7 A is a direct camera image of a damselfly under laser illumination; FIG. 7B is

a numerically reconstructed image from one hologram; FIG. 7C is an image accumulated

from 20 holograms.

FIGS.8A-8C are digitally recorded optical fields: FIG. 8A, a hologram; FIG. 8B, an

object, OO*; FIG. 8C, a reference, RR*.

FIG. 9 is an animation of az-y cross section of the three-dimensional reconstructed

field atx = -1.3 mm, as 20 3D arrays are added in digital interference holography. FIG. 10A are x-y cross sections of the accumulated array at various axial distances z;

FIG. 10B are z-y cross sections of the accumulated array at various x values starting from the

left end of the head, x = 1.84 mm, to near the middle of the head, x = 0.52 mm.

FIG. 11 is an animated three-dimensional reconstruction of the insect's illuminated

surface.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A description of the preferred embodiments of the present invention will now be

presented with reference to FIGS. 1-11.

The apparatus 10 of the present invention is depicted in FIG. 1. A ring dye laser 12

provides a 595.0-nm laser field of ~ 50-mW power with a linewidth of ~ 50 MHz. The laser

beam is expanded with a microscope objective 14 to 20 mm diameter and divided into three

parts using beam splitters 16,18. One of these provides the planar reference beam 20, while

the other two 22,24 constitute the object beam. The object consists of two transparency

targets attached to the back-reflecting mirrors (M) 26,28 in separate optical arms, in order to

avoid obstruction of one object by the other in the same optical path. One target 30 (OBJ1)

is a checkerboard pattern with 2.5-mm grid size, and the other target 32 (OBJ2) is a

transparent letter "A" that fits inside an opaque square of side 13 mm.

The object 22,24 and reference 20 beams are combined in a Michaelson interferometer

arrangement and sent to a translucent Mylar screen S 34. The object distances to the screen

are approximately 149 and 167 cm. The interference pattern on the screen is imaged, for

example, by digital camera 36, such as a Kodak DC 120, through another lens L2 38 for

adjustment of focus and magnification. The exemplary camera 36 has 960 x 1280 pixels with 10x10 μm² pixel size. The calculations presented here use 256 x 256 pixel images of screen

area 13x13 mm, so that the effective pixel resolution on the screen is 51 μm, although this is not intended to be limiting. The corresponding minimum distance for the object is then 1.1

m, in order to accommodate the interference between rays emanating from the two ends of a

13-mm object. For each hologram, the reference beam and the object beam are imaged

separately, so that these images can be subtracted before reconstruction and the resulting images do not contain zero-order terms. It is not attempted to eliminate the conjugate image.

The process is repeated a plurality of times, here up to 11 laser frequencies spaced 1.0 GHz

apart, to achieve a desired axial period A of the resultant hologram images, here 30 cm, and a desired axial resolution δ, here 3.0 cm.

For reconstruction of images, a software package, for example, a MatLab program,

encodes the Fresnel diffraction, which is equivalent to Eq. (2) with appropriate approximations (Goodman, 1968):

E(x,y;z) =exp[ (ik/2z) (x²+y²) ] F{E_Q (x₀,y₀) S (x₀,y₀; z) } [κ_χ, κ_y]

where

S(x,y; z) =-{ik/z) exp[ikz+ (ik/2z) (x²+y²) ]

κ = kx/z, K_y = ky/z, and F{f} [K] represents a Fourier transform/ with respect to the variable

K.

FIGS.2A-2D illustrate the input images of the reference (__, FIG.2 A), the object (O,

using OBJ1, FIG.2B), the interference hologram between the two (H, FIG.2C), and the

subtracted image E = H - R- O (FIG.2D). The holographic image in FIG.2E of the single 17 object is reconstructed at z_x = 149 cm, and shows typical resolution and quality of the reconstructed images (z₀ and z are object and image distances, respectively, measured from

the screen). The remaining fringe pattern inside the squares is due to the out-of-focus twin

image. FIG. 3 A shows the hologram with both objects OBJ1 and OBJ2 on, after subtraction of reference and object images. The images are reconstructed near the two object distances

(FIG. 36) ._;! = 149 cm and (FIG. 3C) z_i2 = 165 cm. The two images are substantially

indistinguishable and contain images of both objects, although it is possible to discern

differences in the sharpness of focus between the two images. The axial resolution determined by focal sharpness is at least - 15 cm, as can be seen in FIG. 4A, where the

vertical axis is a slice of the reconstructed image along the dotted vertical line of FIG. 3C and

the horizontal axis is the image distance z_{ from 140 to 190 cm.

In FIG. 4B two holograms with frequency separation of 1.0 GHz are combined,

showing the expected cosine-squared modulation with a period of 30 cm, whereas in FIG.4C,

two frequencies 2.0 GHz apart are combined and the period is now 15 cm. In FIG. 4D, three

relative frequencies of 0.0, 1.0, and 2.0 GHz are combined, and the narrowing of interference

maxima is evident (cf. FIGS.4B and 4D). Also note that the images of OBJ1 and OBJ2 focus

at different z- locations: The three bright areas near z_λ- = 150 cm (and also at 180 cm) are the

three bright squares of OB Jl's checkerboard, while the bright patch near v = -3.0 mm, z = 165

cm corresponds to the lower left corner of OBJ2's letter "A." Carrying this process further,

eleven holograms with frequencies 0.0, 1.0, 2.0, ... , 10.0 GHz are combined in FIG.4E, which

results in an axial resolution of ~ 3 cm, as expected. The images at two distances are shown in FIG. 5 A for z_n = 149 cm and z_a = 165 cm.

Now each of the images contains only one of OBJ1 or OBJ2, and the out-of-focus images are

substantially suppressed.

The invention thus demonstrates the use of multiwavelength interference of computer-

reconstructed holograms for high axial resolution of three-dimensional images. The apparatus is very simple and amenable to electronic automation without mechanical moving parts. Even

with less-than-optimal laser and imaging systems, the theoretically predicted axial resolution

is easily achieved. The main source of imperfection in FIGS. 4A-4E, for example, was the

mode hop and drift of the nonstabilized laser frequency. Another embodiment may include,

for example, the use of a compact diode laser, direct transfer of an image to a CCD array

surface, and automation of the multiple exposure for speed and stability. The technique can

be applied to both microscopic and telescopic imaging for cross-sectional imaging of objects

of various scales. The cross-sectional images can then be recombined with appropriate scaling for the removal of distortion, resulting in a synthesis of three-dimensional models that can be

subjected to further analysis and manipulation.

In a second embodiment of the present invention, a holographic apparatus 40 (FIG. 6)

comprises a laser, for example, a ring dye laser 41. A portion, here 50 mW, of the laser's

output is passed through a first neutral density filter 42 and is expanded to a predetermined

diameter, here 10 mm, with a beam expander and spatial filter 43.

The beam 90 is apertured 44 to a desired diameter, here 5 mm, and directed to a first

beam splitter 45. A first portion 91 of the split beam passes through a second neutral density

filter 46 and becomes the reference beam 92. A second portion 93 of the split beam is directed to the object 80, here a damselfly specimen, shown under laser illumination in FIG.

6A, wherein the eyes, mouthpiece, and front several legs are visible.

The scattered light 94 from the object 80 is combined with the reference beam 92 at

a second beam splitter 47 to form an interference beam 95, which then passes through a

magnifying lens 48 to image the optical image at the camera' s 49 focal plane 50 onto infinity.

The camera 49, for example, a digital camera (such as model DC290, manufactured by Kodak,

Rochester, NY), is focused at infinity, so that it records a magnified image of the optical

intensity at the plane S 50. The object-to-hologram distance 51 here is 195 mm. The object

beam 94 preferably should be apertured so that it only illuminates the area of the object 80 that

is to be imaged; otherwise, spurious scattering can seriously degrade the contrast and resolution of the reconstructed image.

At a given laser wavelength, three images are recorded: a hologram of the object and reference interference (HH* = | O+R|², FIG. 8 A), the object only (OO*, FIG. 8B), and the

reference only (RR*, FIG. 8C). The laser wavelength is then stepped, starting from λ₀= 601.7

nm at Δλ = 0.154-nm intervals for N=10 steps, so that the expected axial range is A = 2.35 mm and the axial resolution is δ = 0.12 mm.

The digitally recorded images are transferred to a computer 52, where software means

53, for example, a set of MatLab^® scripts, are used for numerical reconstruction. A desired

area, here 4.8 4.8 mm, of the image is interpolated to a 512 x 512 pixel matrix. In an

alternate embodiment, a CCD array is used instead of the camera 49, wherein the image

magnification and interpolation steps are not performed.

The object and reference frames are then numerically subtracted from the hologram

frame, HH*-OO*-RR*, before applying Fresnel diffraction, to eliminate zero-order diffraction. A clean holographic image is then obtained even at 0 ° offset between the object

and reference beams. It is believed that this leaves conjugate images RO* and R*O, but one

of these is substantially completely out of focus and does not appear to interfere with the process of the present invention. The holographic image field is then calculated as above.

The numerical reconstruction and digital interference proceeds by starting from a 512

x 512 pixel, 4.8 x 4.8 mm digital hologram (with zero-order subtraction). The Fresnel

diffraction patterns are calculated at N+l = 21 z values, z = Z + mδ, where Z, = 195 mm is

the original object distance 51 and m = -10, -9,..., 9, 10. This results in a 3D array of 512 x

512 x 21 pixels and a 4.8 x 4.8 x 2.35 mm volume, representing the holographic optical field

variation in this volume.

This process is repeated for 20 sets of triple digitally recorded images at 20 different

wavelengths. At this point, the field patterns in the individual 3D arrays show little variation

along a few millimeters of the z direction. Then the 203D arrays are numerically superposed

by adding the arrays elementwise, resulting in the accumulated field array of the same size.

This new array then has a field distribution that represents the 3D object structure, as

described previously. In practice, owing to the laser's frequency fluctuation and imprecision

of the wavelength intervals, there is a random phase variation among the 20 calculated field

arrays. This may be corrected by introducing a global phase factor into each of the 3D arrays

before carrying out the summation.

FIG. 7B is an example of a 2D holographic image reconstructed from a single

hologram at Z, = 195 mm. Imaging of diffuse scattering objects, such as the biological

specimen of this exemplary illustration, using coherent illumination gives rise to speckle 21 noise, causing degradation of contrast and resolution. This can be reduced somewhat by

optimizing the illumination aperture and the overall stability of the optical system.

The effect of digital interference is illustrated in FIG. 9. The animation frames show a 2.35 x 4.8 mm z-y cross section at x = -1.3 mm, as the holographic field arrays are added on

top of each other from 1 to 20. When N= 1 , the z variation is due to a small diffraction of the

field, but at N= 2 the field exhibits cosine variation in the z direction, with a different phase origin depending upon the object-to-surface distance. As further arrays are added, the cosine

pattern becomes similar to δ-function spikes in the z direction. When all 20 field arrays are

accumulated, only one z value has a significant intensity above noise for each object surface

pixel.

FIGS. 10A and 1 OB show cross-sectional tomographic views of the accumulated field

array, with FIG. 10A showing x-y cross sections as the axial distance z is varied from the front

tip of the mouthpiece to the back of the eyes, over a distance of 2.35 mm. FIG. 10B shows

z-y cross sections as the x value is varied from 1.84 to 0.52 mm, or from the edge of the

insect's left eye to the middle of the face.

The contrast of these images is numerically enhanced by taking the logarithm and

applying thresholding to the calculated field arrays. Thus tomographic imaging by

wavelength-scanning digital interference is clearly demonstrated. The accumulation of N

holographic field arrays has an additional benefit of averaging out the coherent speckle noise.

FIG. 7C is obtained by starting from the accumulated array and summing over the z

direction, yielding a 2D image of the object 80. The resulting image quality approaches that

of the photographic image of FIG. 7A, and the speckle noise is substantially completely

removed. Further, each object surface element is imaged in focus regardless of the depth of focus of the optical system. This feature is especially beneficial in an embodiment applied to microscopic imaging with a large numerical aperture.

An animated 3D reconstruction of the object's illuminated surface is made by plotting

the brightest volume elements in 3D perspective (FIG. 11). As the azimuthal angle rotates,

the two eyes and mouthpiece are recognizable as being the most prominent features. Two or

three front legs are also visible, although there appear to be ghost images present.

This embodiment has demonstrated three-dimensional imaging of a small biological

specimen using wavelength-scanning digital interference holography. Cross-sectional images

of the object are generated with clear focus and suppression of coherent speckle noise. The

resolutions achieved are ~ 100 μm in the axial direction and tens of micrometers in the lateral direction, as defined by the optical system and computer capacity of the present embodiment,

and are thus not intended as limitations. With a semitransparent microscopic object, full tomographic imaging is possible.

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Claims

What is claimed is:

1. A method for imaging a three-dimensional object comprising the steps of:

(a) illuminating an object with radiation at a wavelength to form a reflected image beam;

(b) providing a reference beam comprising the wavelength;

(c) recording an interference pattern between the reference beam and the image beam;

repeating steps (a)-(c) at a succession of different wavelengths separated by a

predetermined wavelength step; computing a holographic image from the interference pattern for each wavelength; and

adding the holographic images together to form an intensity distribution

pattern.

2. The method recited in Claim 1 , further comprising the steps of:

extracting out a series of two-dimensional cross-sectional images from the

intensity distribution pattern;

correcting microscopic image distortion in the cross-sectional images; and

reassembling the cross-sectional images into a three-dimensional model of the

object.

3. The method recited in Claim 1, wherein the illuminating step comprising

illuminating the object with coherent radiation.

4. The method recited in Claim 3, further comprising the step of expanding the

coherent radiation prior to the illuminating step.

5. The method recited in Claim 1 , wherein the predetermined wavelength step

comprises a function of an axial scale of the object.

6. The method recited in Claim 1, further comprising the step of subtracting a

zero-order intensity from each computed holographic image prior to the adding step.

7. The method recited in Claim 6, further comprising the steps of:

(d) recording an image of the object only; and

(e) recording an image of the reference beam only; and wherein:

the repeating step further comprises repeating steps (d) and (e) at the

succession of different wavelengths; and

the subtracting step comprises subtracting the object-only and reference-beam-

only images from the interference pattern.

8. The method recited in Claim 7, wherein the computing step comprises

calculating a holographic image field at each wavelength using a Fresnel diffraction formula.

9. The method recited in Claim 1, wherein the object comprises two two-

dimensional objects positioned different distances from a source of the radiation, and further comprising the step of extracting out two two-dimensional cross-sectional images from the

intensity distribution pattern, each image representative of one of the objects.

10. The method recited in Claim 9, wherein the extracting step comprises encoding

the Fresnel diffraction as a function of a Fourier transform with respect to radiation wavelength.

11. A system for imaging a three-dimensional object comprising:

illumination means tunable between a first wavelength and a second wavelength;

means for splitting radiation from the illumination means into an object beam

and a reference beam;

means for directing the object beam to illuminate an object desired to be imaged to form an image beam;

means for recording an interference pattern between the reference beam and the image beam;

means for computing a holographic image from the interference pattern for the

first ad the second wavelength; and

means for adding the holographic images together to form an intensity distribution pattern.

12. The system recited in Claim 11 , wherein the illumination means comprises a

source of coherent radiation.

13. The system recited in Claim 12, wherein the radiation source comprises a ring

dye laser.

14. The system recited in Claim 11, further comprising means for magnifying

radiation from the illumination means prior to the splitting means.

15. The system recited in Claim 11 , further comprising means for aperturing the

object beam to a desired area.

16. The system recited in Claim 15, wherein the desired area comprises an area

substantially equal to an area of the object desired to be imaged.

17. The system recited in Claim 11, wherein the recording means comprises at

least one of a digital camera or a charge-coupled-device array.

18. The system recited in Claim 11 , further comprising means for magnifying the

interference pattern positioned between the magnifying means and the recording means.

19. The system recited in Claim 11 , further comprising a first neutral-density filter

positioned to filter the radiation between the illumination means and the splitting means.

20. The system recited in Claim 11 , further comprising means for combining the

reference beam and the image beam to form the interference pattern therebetween.