Orientation-independent differential interference contrast … · OCIS codes: 180.0180, 100.2980, 170.1530, 170.3010, 170.3890, 170.3880. 1. Introduction Differential interference

Orientation-independent differential interferencecontrast microscopy

Michael Shribak and Shinya Inoué

We describe a new technique for differential interference contrast (DIC) microscopy, which digitallygenerates phase gradient images independently of gradient orientation. To prove the principle weinvestigated specimens recorded at different orientations on a microscope equipped with a precisionrotating stage and using regular DIC optics. The digitally generated images successfully displayed andmeasured phase gradients, independently of gradient orientation. One could also generate images show-ing distribution of optical path differences or enhanced, regular DIC images with any shear direction.Using special DIC prisms, one can switch the bias and shear directions rapidly without mechanicallyrotating the specimen or the prisms and orientation-independent DIC images are obtained in a fractionof a second. © 2006 Optical Society of America

OCIS codes: 180.0180, 100.2980, 170.1530, 170.3010, 170.3890, 170.3880.

1. Introduction

Differential interference contrast light microscopy(DIC) is widely used to observe structure and motionin unstained living cells and isolated organelles. DICmicroscopy uses an interference optical system inwhich the reference beam is sheared laterally by asmall amount, generally by somewhat less than thediameter of the Airy disk. The technique produces amonochromatic shadow-cast image that displays thegradients of optical paths in the specimen. Those re-gions of the specimen where the optical paths in-crease along a reference direction appear brighter (ordarker), while regions where the path differences de-crease appear in reverse contrast. As the gradient ofthe optical path grows steeper, image contrast is ac-cordingly increased. Another important feature ofDIC imaging is that it produces effective optical sec-tioning.1 This is particularly obvious when high-numerical-aperture (NA) objectives are used togetherwith high-NA condenser illumination.

The DIC technique was invented by Smith2 in1947. He placed between a pair of polarizers one Wol-laston prism at the front focal plane of the condenser

and another Wollaston prism in the back focal planeof the objective lens. The first Wollaston prism splitsthe input beams angularly into two orthogonally po-larized beams. The condenser makes the beam axesparallel, with a small shear. Then the objective lensjoins them in the back focal plane where the secondWollaston prism introduces an angular deviation intothe beam and makes them parallel. Thereafter bothof the two orthogonally polarized beams are recom-bined into one beam. This optical configuration cre-ates a polarizing shearing interferometer, by whichone visualizes phase gradients of the specimen underinvestigation.

In conventional medium- to high-NA objectivelenses, the back focal plane is located inside the lenssystem and therefore is not available for insertion ofa Wollaston prism. If the Wollaston prism is placedfar from the back focal plane, the prism only makesthe rays parallel, but those beams are spatially dis-placed and hence are not recombined. Therefore theSmith DIC scheme requires a special design for themicroscope objective lenses such that the Wollastonprism can be incorporated within.

Nomarski, who proposed a modified Wollastonprism in 1952, provides an alternative solution.3,4

The Nomarski prism simultaneously introduces aspatial displacement and an angular deviation of theorthogonally polarized beams. The prism thereforecan be placed outside the objective lens. By usingcrystal wedges with appropriately oriented axes, theNomarski prism recombines the two beams (sepa-rated by the condenser Wollaston) as though a regu-

The authors are with the Marine Biological Laboratory, WoodsHole, Massachusetts. M. Shribak’s e-mail address is [email protected].

Received 25 February 2005; revised 30 August 2005; accepted 1September 2005.

0003-6935/06/030460-11$15.00/0© 2006 Optical Society of America

460 APPLIED OPTICS � Vol. 45, No. 3 � 20 January 2006

lar Wollaston prism were located in the proper planein the objective lens. The Nomarski DIC scheme canbe used in conjunction with regular high-NA micro-scope objectives, which exhibit low stress birefrin-gence.

Video-enhanced DIC permits enhancement of con-trast while it removes unwanted background signal(such as fixed image noise caused by dust particles,nonuniform illumination, or other imperfections inthe optical system) by subtraction of a reference im-age with no specimen.5 Also, Inoué6 and Allen et al.7applied similar enhancement techniques to improvecontrast in polarization microscopy.

Holzwarth et al. developed video-enhanced DIC mi-croscopy with polarization modulation.8,9 Switchingthe polarization of the incident light in alternate videoframes with a computer-controlled liquid-crystal vari-able retarder increased the contrast signal of un-stained biological specimens by a factor of 2 relative tothe standard video-enhanced DIC. The modulatorswitches image highlights into shadows and vice versa.Subtracting alternate frames creates a difference DICimage in which contrast is doubled while image defectsand noise are canceled.

These regular DIC techniques show the two-dimensional distribution of optical path gradients asobserved for a particular shear direction. The con-trast of DIC images is thus not symmetrical; it variesproportionally with the cosine of the angle betweenthe azimuth of the specimen gradient and the direc-tion of the wavefront shear. It is therefore prudent toexamine unknown objects at several azimuths.4,10

Preza used two, four or eight conventional DICimages at different shear directions but with thesame bias in an iterative phase-estimation method tocalculate the specimen’s phase function.11 She did notuse images with inverse biases because she supposedthat they can be useful in reduction of noise only. Theproposed theory was simulated by mathematicalmodels that employ a large amount of shear (near theAiry radius) and large bias, ��2. A thin specimenwith 0.7 �m thickness was investigated with a 0.5NA objective lens.

To overcome the limitations of existing systems wedevised an orientation-independent DIC system,which requires no mechanical movement of the DICprisms or of the specimen.12 To explore the utility ofsuch a system by using immediately available compo-nents, we recorded several images with the specimenoriented in different directions, followed by digitalalignment and processing of the images. Through com-putation we generated two separate images, whichshow, the magnitude distribution of the optical pathgradients and their azimuths. As described in Section3 below, the two images can be viewed separately orcombined into one color shadow-cast picture, e.g., withthe brightness representing magnitude and colorshowing azimuth, respectively. The images obtainedare independent of specimen orientation and free fromgray background. Furthermore, we show how it is pos-sible to generate quantitative phase images (showingdistribution of optical paths) as well as enhanced reg-ular DIC images with any shear direction from theorientation-independent DIC data.

2. Principles of Orientation-IndependentDIC Microscopy

A. Theoretical Model of DIC Image

A schematic of ray paths in a DIC microscope isshown in Fig. 1. The polarizer creates a linearly po-larized beam that contains two components, Ex

and Ey, with equal intensities, and the retarder in-troduces a variable phase shift, �, between the com-ponents. Then the first Wollaston prism splits thebeam and the second Wollaston prism combines thesplit beam, as described in Section 1.

A DIC image can be modeled as the superpositionof one image over an identical copy that is displacedby a differential amount � and phase shifted by bias�. For example, point A in the first image will besuperimposed with point B in the copy of the image(Fig. 1). For simplicity consider a pure (nonbirefrin-gent) phase specimen, which is described in Carte-sian coordinates XOY in the object plane. If theoptical path distribution in the first image is ��x, y�,

Fig. 1. Conventional DIC microscope setup: Sc, monochromatic light source; P(45°), polarizer at 45° azimuth; R(�, 0°), retarder at 0°azimuth and phase shift �; WP1, Wollaston prism 1 with splitting angle ε1; C, condenser lens with focal distance fc; Sp, object underinvestigation with OPD � � between points A and B; O, objective lens with focal distance fob; WP2, Wollaston prism 2 with splitting angleε2; A(�45°), analyzer at �45° azimuth; Ex, Ey polarization components; �, amount of shear.

20 January 2006 � Vol. 45, No. 3 � APPLIED OPTICS 461

then the second displaced image has the optical pathdistribution ��x � �x, y � �y�. Here �x and �y areprojections of shear vectors on the corresponding co-ordinate axes. The optical path difference (OPD) be-tween the two images can then be written as

OPD�x, y� � ��x, y� � ��x � �x, y � �y�. (1)

Taking into account that the shear distance is a smallvalue (approximately half of the optical resolutionlimit), we can write the optical path distribution inthe displaced copy ��x � �x, y � �y� in the followinglinear approximation:

��x � �x, y � �y� � ��x, y� � ��x, y�, ��, (2)

where the last term on the right-hand side is thescalar product of two vectors.

��x, y� � grad��x, y�� x, y�x ,

��x, y�y

is a gradient of the optical path and � � (�x, �y) is ashear vector.

Thus a phase difference distribution between twooverlapping images ��x, y� is described by the for-mula

��x, y� �2�

( � (��x, y�, �))

�2�

( � ��x, y�cos �x, y�), (3)

where � is the wavelength, �x, y� is the angle be-tween the shear direction and the optical pathgradient, and ��x, y� � |��x, y�| is the gradient’smagnitude.

The intensity distribution in the image, which isthe result of interference of the two beams, is

I�x, y� �12 I[1 � cos(2�

� ��x, y�

� cos ��x, y� � ��)] � Imin, (4)

where I is the beam’s intensity before it enters thefirst DIC prism, ��x, y� is the gradient azimuth, and �is the shear azimuth [here we used �x, y� ��x, y� � �].

From Eq. (4), if the shear direction coincides withthe optical path gradient � � 0° or � 180°� thepicture contrast is maximal. When the shear direc-tion is oriented perpendicular to the gradients � � 90° or � 270°�, the intensity contrast becomeszero.

Equation (4) does not take into consideration therefraction of the beam in a thick nonhomogeneousspecimen or changes of intensities and phase owingto birefringence. Therefore a quantitative interpreta-

tion of the results will work better with a thin, low-birefringence specimen.

B. Six-Frame Processing Algorithm

To find the two-dimensional distribution of magni-tude and azimuth of optical path gradients we canapply a technique similar to the one that we devel-oped for orientation-independent polarization mi-croscopy.13 For instance, we take the next four rawimages with 90° step differences in the shear orien-tation and with the same bias �, and two raw imageswith no bias:

� � 0°,

I1 �12 I�1 � cos�2�

� � �� cos �� Imin;

� � 90°,

I2 �12 I�1 � cos�2�

� � �� sin �� Imin;

� � 180°,

I3 �12 I�1 � cos�2�

� � �� cos �� Imin;

� � 270°,

I4 �12 I�1 � cos�2�

� � �� sin �� Imin;

� � 0° or � � 180 °,

I0� �12 I�1 � cos�2�

�� cos �� Imin;

� � 90° or � � 270 °,

I0� �12 I�1 � cos�2�

�� sin �� Imin. (5)

Then compute the following two terms:

A �I1 � I3

I1 � I3 � 2I0�tan��

�� tan�2�

�� cos ��,

B �I2 � I4

I2 � I4 � 2I0�tan��

�� tan�2�

�� sin ��. (6)

Using these terms, we can find the exact solutionfor gradient magnitude and azimuth distributions��x, y�and ��x, y�, respectively:

��x, y� �

2�� arctan A�2 � �arctan B�2�1�2,

��x, y� � arctan�arctan Barctan A�. (7)


1. Four-Frame Processing AlgorithmIn some cases, fewer than six images are collectedto support calculation of orientation-independentvalues and images. Some approximations may berequired for completion of the calculations. For ex-ample, if the product of shear distance and gradientmagnitude is small ��2�� 1�, Eq. (4) can besimplified to

I�x, y� �12 I�1 � cos�2�

��

2�

�� sin�2�

�

� cos��x, y� � �� Imin. (8)

Then four images can be collected and modeled as

� � 0°,

I1 �12 I�1 � cos�2�

��

2�

�� sin�2�

�cos �� Imin;

� � 90°,

I2 �12 I�1 � cos�2�

��

2�

�� sin�2�

�sin �� Imin;

� � 180°,

I3 �12 I�1 � cos�2�

��

2�

�� sin�2�

�cos �� Imin;

� � 270°,

I4 �12 I�1 � cos�2�

��

2�

�� sin�2�

�sin �� Imin;

(9)

Thus the next two equations permit calculationof the two-dimensional distribution of the gradientmagnitude and azimuth of optical paths in the spec-imen; these can be imaged separately and indepen-dently of the shear direction:

��x, y� �

2��tan��

��I1 � I3

I1 � I3�2

� �I2 � I4

I2 � I4�21�2

,

��x, y� � arctan�I2 � I4

I1 � I3�. (10)

Here we have assumed that the microscope hasmoderately high extinction �I�Imin � 200� and thushave neglected Imin in the divisors of the first of Eqs.(10).

Note that the two algorithms considered above em-ploy ratios between intensities of light that has in-teracted with the specimen. Therefore they suppresscontributions of absorption by the specimen, nonuni-formity of illumination, etc., which can otherwise de-teriorate a DIC image.

C. Two-Frame Processing Algorithm

Other numbers of specimen images, for instance two orthree can also be used for calculating the magnitudeand azimuth of the gradient. For example, two speci-men images and three background images can be col-lected and modeled according to Eq. (8):

� � 0°,

I1 � I sin��

��sin��

��

2�

�� cos��

�cos �

� Imin;

� � 90°,

I2 � I sin��

��sin��

��

2�

�� cos��

�sin �

� Imin; (11)

and background images without the specimen:

� � 0°, Ibg1 � I sin2��

�� Imin,

� � 90°, Ibg2 � I sin2��

�� Imin; (12)

for � 0 and an arbitrary �, Ibg0 � Imin.Values K and L are calculated as follows:

K �I1 � Ibg1

Ibg1 � Ibg0tan��

�

�

I2�

�� sin��cos��cos �

I sin2��

� tan�� 2�

�� cos �,

L �I2 � Ibg2

Ibg2 � Ibg0tan��

�

�

I2�

�� sin��cos��sin �

I sin2��

� tan�� 2�

�� sin �. (13)

Then the gradient magnitudes ��x, y� and azimuthdistributions ��x, y� can be obtained from the follow-ing formulas:

��x, y� �

2��A2 � B2,

��x, y� � arctan�BA�. (14)


Further approximations can be employed, for exam-ple, to simplify the calculations or to reduce the num-ber of collected background images. For example, ifIbg0 is small it can be omitted from the above equa-tions.

Using just two specimen images for obtainingorientation-independent DIC data increases thespeed of measurement. However, the sensitivity be-comes lower. Moreover, the algorithm does not useratios between intensities of light that has interactedwith the specimen. Therefore this algorithm can beused only when the specimen’s absorption is negligi-ble and illumination is highly stable and uniform.

D. Using Orientation-Independent DIC Data to ObtainEnhanced Regular DIC and Phase Images

After computing the optical path gradient distribu-tion we can restore enhanced regular DIC imagesIenh�x, y� with any selected shear direction �:

Ienh�x, y� � 1 � cos(2�

� ��x, y�cos ��x, y�

� ��). (15)

The enhanced image, Ienh�x, y�, provides a calculatedimage for any desired shear direction � without therequirement to collect an image directly for thatshear direction. Moreover, the enhanced image willhave less noise than a regular DIC image. In addi-tion, it suppresses deterioration of the image causedby specimen absorption and illumination nonunifor-mity.

We can obtain the distribution of optical phase��x, y� in the specimen by computing the followingline integral14:

��x, y� �2�

�C

��x�, y��cos ��x�, y��dx�

� ��x�, y��sin ��x�, y��dy��. (16)

As the simplest contour for integration we can chooserectangular ones along the coordinate axes:

��x, y� �2�

��0

x

��x�, 0� cos ��x�, 0� dx�

��0

y

��x, y��sin ��x, y��dy�. (17)

Here we assign zero phase to the beginning point ofthe coordinate.

Where calculations are performed in terms of pix-els, Eq. (17) can have the following form:

�mn �2�

��k�1

n

�0k cos �0k � �p�1

m

�pn sin �pn�, (18)

where m and n are row and column numbers of thepixels and �mn is the value of the optical phase forpixel m, n.

Other techniques for phase computation can alsobe used, for instance, iterative computation,11 nonit-erative Fourier phase integration,15 or nonlinear op-timization with hierarchical representation.16

Biggs17 and colleagues have developed an iterativedeconvolution approach to the computation of a phaseimage that follows the same principles as the decon-volution techniques normally used to remove out-of-focus haze.18 In the case of DIC imagery, if the imagebackground is removed such that the data have a zeromean, then the point-spread function can be modeledas a positive and a negative Dirac delta function withsmall separation between them.11 If the specimen isnot a purely phase object and contains absorbing struc-tures, then four DIC images with 90° differences inorientation should be collected. The two sets of oppo-site orientation can be used to separate the phase-difference information from the amplitude modulation,which reduces potential artifacts in the reconstruction.This preprocessing is also valuable when small biasretardations are used to maximize image contrast,which also results in a highly nonlinear intensity re-sponse to phase differences.

The Biggs optimization is based on minimizing theleast-squares error between the observed phase dif-ferences and the DIC image recalculated from theestimated phase map. For a two-image reconstruc-tion, the errors from each are combined to form asingle metric. We solve the single phase image iter-atively by minimizing the error metric, using a gra-dient descent optimization with acceleration,19 withtypically 100 iterations required. A conjugate gradi-ent or other optimization approach could also be em-ployed. Depending on the specimen used, a penaltyterm can also be introduced to minimize negativephase values with respect to the background if thatinformation is known a priori. The reconstructionprocess thus far has not taken into account any effectof diffraction or other optical effects that limit theobservable resolution in the image. Once the phasemap is calculated, the image is further deconvolvedby use of an iterative blind deconvolution algorithmthat is able to determine the amount of blur directlyfrom the image provided and use this PSF to improvethe resolution of the image. Once the point-spreadfunction is known, only five iterations are typicallyrequired. The algorithm is commercially available inthe AutoDeblur software from AutoQuant Imaging(Troy, New York).

3. Experimental Verification

A. Description of the Experiment

For verification of theoretical analysis, we carried outseveral experiments, using artificial and biologicalspecimens. We employed the universal (polarized)light microscope (ULM, or ShinyaScope) that hasbeen developed by one of us over five decades and thatis one of the most sophisticated and versatile light


microscope platforms available today.1 The micro-scope is optimized for polarization imaging and in-cludes a precision stage that permits rotation of thespecimen with fractional micrometers of eccentricityor focal shift. The ULM is equipped with a high-brightness fiber illuminator. A 100 W concentratedmercury arc lamp coupled with a green 546 nmbandpath-filter was employed during the experi-ments. For the test published here, we used a Nikon20� objective with a NA of 0.75 and a Nikon Univer-sal Achromatic-Aplanat condenser with its NA of 1.4stopped down to match the objective’s NA. Imageswere collected with a Hamamatsu C5985 chilled CCDcamera or a Hamamatsu C4742-95 high-resolutiondigital CCD camera.20 The resolution of the micro-scope, which is determined by the ratio 1.22��2 NA�,was 0.44 �m, and the depth of field according to theratio n�NA2 was 1.5 �m, where n is the refractiveindex of the objective lens immersion medium.1

We acquired four regular DIC images of the spec-imen with the same bias at 90° orientation difference,and two images without bias, as described in Section2. In addition, we took corresponding backgroundDIC images without the specimen in the field of view.The regular DIC images were aligned by use of Im-ageJ software.21 The background images were used tocompensate for nonuniformity in the intensity distri-bution of the illumination beam, because otherwiseeach part of the specimen could be exposed to differ-ent light intensities during rotation of the specimen.

Using Eqs. (7), (15), and (18), we computed imagesof gradient magnitude and azimuth distributions ofoptical paths, optical phase distribution, and en-hanced regular DIC image with any chosen sheardirection. For the computation we used Mathematicasoftware.22

B. Orientation-Independent DIC Images of MicroscopicGlass Rods Embedded in an Immersion Medium

First we explored a model specimen, which is opti-cally similar to transparent filaments in living organ-isms. We took short segments of glass rods, which areused as spacers in liquid-crystal cells, and embeddedthem in Fisher Permount mounting medium (FisherScientific Company, http://www.fishersci.com). Therefractive indices of the glass rods and the Permountat wavelength 546 nm were measured with a Jamin–Lebedeff microscope (Zeiss, Germany), and were1.554 and 1.524, respectively. A drop of the suspen-sion was placed between a microscope slide and a0.17 mm thick coverslip, and the preparation wasplaced on the precision rotating microscope stage.

One of the images taken by regular DIC optics isshown in Fig. 2. Also, the figure contains line scans ofintensities in two sections; one of them (AA=) isscanned along the shear direction and the other (BB=)is perpendicular the shear direction. Both scans arenormalized to the maximal intensity in the image.

Gray-scale images of gradient magnitude com-puted from Eqs. (7) are given in Fig. 3. Here bright-ness is linearly proportional to the magnitude. The

absolute magnitude value was not determined, be-cause the exact amount of the shear was unknown.The gradient magnitude values measured along linesA-A= and B-B= are shown by filled circles (Fig. 3,right). Unlike in Fig. 2, the two linear scans ofmagnitude now exhibit virtually no difference. Thegradient magnitude image clearly shows the rodboundaries independently of orientation.

For preliminary analysis of the experimental datawe employed a simple model for a DIC image of glassmicrospheres as described by Resnick.23 For analysisof DIC images he used a model that comprised 2 �mdiameter microspheres with a 100��1.4 objectivelens. The spherical model can also be used for a (one-dimensional) glass rod, which is oriented parallel tothe object plane. This model does not take into ac-count refraction of rays, microscope resolution, out-

Fig. 2. Regular DIC image of 4 m diameter glass rods immersedin Permount. The DIC shear direction is parallel to AA= (left).Linear scans of normalized intensity in sections A-A= and B-B= areshown at the right.

Fig. 3. Computed gradient magnitude image of the glass rods(left). Linear plots of normalized gradient magnitude in sectionsA-A= and B-B= are shown at the right. The experimental data areindicated by filled circles. The solid curves show the theoreticalresults calculated with simplified assumptions (see text).


of-focus contributions in the thick specimen, changesin polarization, etc.

Assume that the center of the Cartesian coordinatecorresponds to the center of the rod, the Y axis isparallel to the rod axis, and the Z axis is directedalong the microscope axis. The relative phase retar-dation (in radians) experienced by a ray travelingthrough the rod along the microscope axis is as fol-lows23:

��x� �4�

�nr � nm��r2 � x2 � �max�1 � �x � r�2, (19)

where �max � �4��nr � nm�r, r is the diameter ofthe rod, and nr and nm are the refractive indices of therod and the surrounding media, respectively.

When two rays are spatially displaced along the Xaxis by a small distance � �� r, the magnitude ofgradient between them can be determined by thefollowing formula:

��x� ��x � �� x�

��

2��nr � nm�

��0 x � �r or x � r � �

�r2 � x2 �r � x � �r � �

��r2 � x2 � �r2 � �x � ��2� �r � � � x � r

�r2 � �x � ��2 r � x � r � �

.

(20)

The maxima of function ��x� occur at x � �r � �and x � r. For � �� r,

�max � 2�2�nr � nm��r � �.

Then the normalized gradient magnitude can be writ-ten as

��x��max �1

�2r�

��0 x � �r or x � r � �

�r2 � x2 �r � x � �r � �

��r2 � x2 � �r2 � �x � ��2� �r � � � x � r

�r2 � �x � ��2 r � x � r � �

.

(21)

Theoretical plots of the normalized gradient magni-tude are shown by the solid curves in Fig. 3 (right).We used r � 2.1 �m for section A-A= and r� 2.0 �m for section B-B=. The shear distance intro-duced by the microscope’s DIC prisms was unknownand was estimated to be 0.2 �m for these examples.The experimental results show a better correspon-dence for higher values of the gradient magnitude.However, for lower values the experimental data arewider than the theoretical curve by �0.5 �m. Thisfact indicates that the theoretical model needs to be

improved by taking into account the Airy disk’s ra-dius �0.44 �m at a N.A. of 0.75�, the distance (0.31m) between the beam and the contact points of theperipheral rays with the rod, etc.

Both the gradient magnitude and the azimuth im-ages can be combined into one color-shaded picture,e.g., with the brightness representing magnitude andthe color showing azimuth (Fig. 4). As can be seenfrom the shaded color, a gradient vector on the rodboundaries is always oriented toward the rods. Thatmeans that the rod’s refractive index is higher thanthe refractive index of the Permount.

Using the simple numerical contour integration de-scribed in Eq. (17), we computed the two-dimensionalphase distributions ��x, y� of rays transmitted thr-ough the glass rods (Fig. 5, left). The reconstructedphase image contains some streaks, which can becaused by misalignment of the raw DIC images. Thenormalized phase values ��x, y��max� along linesA-A= and B-B= are shown by filled circles (Fig. 5,right).

C. Orientation-Independent DIC Imaged Microstructureof the MBL–NNF Test Target

We investigated another specimen: a test target de-veloped at the Marine Biological Laboratory, WoodsHole, Mass., in collaboration with the NationalNanofabrication Facility at Cornell University.24

The specimen has a 90 nm thick SiO2 film depositedonto a number 1 1/2 glass coverslip. The film wastreated to remove SiO2 from regions exposed to theelectron beam by microlithography. Then the cover-slip was cemented with the target directly lyingagainst the inside surface of a 1 mm thick regularmicroscope slide. The target includes a 75 �m diam-

Fig. 4. Computed gradient image of the same group of glass rodswith the azimuth in pseudocolor. The color wheel at the lower leftcorner depicts the gradient azimuth.


eter Siemens test star that consists of 36 wedge pairs.The period near the outer edge is 6.5 �m, decreasinglinearly toward the center. The optical path differ-ence between the etched structure and the film wasmeasured with a Jamine–Lebedeff microscope. Itequals 60 nm.

In Fig. 6 we show a regular DIC image (left), thecomputed gray-scale gradient magnitude image (cen-ter), and the phase of the MBL-NNF test target(right). In the rightmost figure the dark star imageand the light background show that the refractiveindex in the star wedges is lower than in the sur-

rounding silicon dioxide film. The lower portions ofthe figure show line scans of intensity in the regularDIC image, the gradient magnitude image, and thephase image along the same section. The plots arenormalized to the maximum intensity values.

D. Orientation-Independent DIC Images of Fixed BovinePulmonary Artery Endothelial Cell

The analytical technique has been used with severalbiological specimens. One of them was a preparedmicroscope slide (F-14780) containing bovine pulmo-nary artery endothelial cells stained with a combina-tion of fluorescent dyes (Molecular Probes, Inc.,Eugene, Ore., http://www.probes.com).

Figure 7 demonstrates a regular DIC image of a cell,the computed gradient magnitude image, and the com-puted phase image. The orientation-independent DICimages clearly reveal the refractive boundaries anddetailed structures of the cell. The phase image showsthe dry mass distribution of the cell regions underinvestigation.

In Fig. 8 we present enhanced regular DIC imagesof the same bovine epithelial cell with various sheardirections at every 45°, which are computed from thegradient data. The images show the changes in con-trast and gray shading of different parts of the cell asthe computed shear direction is altered. In these dig-itally enhanced DIC images, the empty areas have31% less optical noise than the original DIC images.

These results demonstrate that the proposed DICtechnique can successfully image and measure phasegradients as well as the distribution of phase retar-dances (OPDs) of transparent specimens, indepen-

Fig. 5. Computed phase of the glass rods (left). Linear scans ofnormalized phase in sections A-A= and B-B= are shown at the right.The experimental data are indicated by filled circles. The solidcurves show the theoretical results.

Fig. 6. Regular and computed orientation-independent DIC images of Siemens star and line scans along section AA=. The phase imageof the Siemens star was calculated by D. Biggs (AutoQuant Imaging, Inc., Troy, N.Y.).


dently of the directions of the gradient and minimallyinfluenced by specimen absorption.

4. Conclusions

1. We have developed the theoretical basis fororientation-independent differential interference con-trast microscopy. The new approach facilitates preciseanalyses of organelle morphology motility, and shapechanges as well dry mass distribution, e.g., in un-stained living cells.

2. Using regular DIC optics and a microscopeequipped with a precision rotating stage, we con-firmed the theoretical validity of the proposed tech-nique.

3. Since the manuscript of this paper was submittedfor publication, U.S. patent application 2005-0152030,“Orientation-independent differential interference

contrast microscopy technique and device,” was pub-lished on 14 July 2005.12 The patent describes designsfor achieving orientation-independent DIC images byusing novel arrangements of optical and electro-opticalcomponents, without the need for any mechanical re-orientation or adjustments of the DIC prisms or of thespecimen. We estimate that using the new device andthe algorithms described in the current paper will al-low orientation-independent DIC images to be digi-tally generated in a fraction of a second.

The authors thank David Biggs and Mike Meichleof AutoQuant Imaging, Inc., for helpful discussionsand for providing deconvoluted phase images. Weare also grateful to Rudolf Oldenbourg of the Ma-rine Biological Laboratory and to James LaFoun-

Fig. 7. Regular and computed orientation-independent DIC images of bovine pulmonary artery endothelial cell. The phase image of thebovine cell was calculated by D. Biggs (AutoQuant Imaging, Inc., Troy, N.Y.).

Fig. 8. DIC images of bovine pulmonary artery endothelial cell with various shear directions computed from orientation-independent DICdata.


tain of the University of Buffalo for their encou-ragement and support.

References and Notes1. S. Inoue and K. R. Spring, Videomicroscopy: The Fundamen-

tals, 2nd ed. (Plenum, 1997).2. F. H. Smith, “Interference microscope,” U.S. patent 2,601,175

(17 June 1952).3. G. Nomarski, “Interferential polarizing device for study of

phase object,” U.S. patent 2,924,142 (9 February 1960).4. R. D. Allen, G. B. David, and G. Nomarski. “The Zeiss–Nomarski

differential equipment for transmitted light microscopy,” Z.Wiss. Mickrosk. 69(4), 193–221 (1969).

5. R. D. Allen, N. S. Allen, and J. L. Travis, “Video-enhancedcontrast differential interference contrast (AVEC-DIC) mi-croscopy: a new method capable of analyzing microtubule-related motility in the reticulopodial network of Allogromialaticollaris,” Cell Motil. 1, 291–302 (1981).

6. S. Inoué, “Video image processing greatly enhances contrast,quality, and speed in polarization-based microscopy,” J. CellBiol. 89, 246–356 (1981).

7. R. D. Allen, J. L. Travis, N. S. Allen, and H. Y. Imaz, “Video-enhanced contrast polarization (AVEC-POL) microscopy: anew method applied to detection of birefringence in motilereticulopodial network of Allogromia laticollaris,” Cell Motil.1, 275–289 (1981).

8. G. Holzwarth, S. C. Webb, D. J. Kubinski, and N. S. Allen,“Improving DIC microcopy with polarization modulation,” J.Microsc. (Oxford) 188, 249–254 (1997).

9. G. Holzwarth, D. B. Hill, and E. B. McLaughlin, “Polarization-modulated differential-interference contrast microscopy with avariable retarder,” Appl. Opt. 39, 6288–6294 (2000).

10. M. Pluta, ed., Specialized Methods, Vol. 2 of Advanced LightMicroscopy (Elsevier, 1989),

11. C. Preza, “Rotational-diversity phase estimation fromdifferential-interference-contrast microscopy images,” J. Opt.Soc. Am. A 17, 415–424 (2000).

12. M. Shribak “Orientation-independent differential interference

contrast microscopy technique and device,” U.S. patent appli-cation 2005-0152030 (14 July 2005).

13. M. Shribak and R. Oldenbourg, “Technique for fast and sen-sitive measurements of two-dimensional birefringence distri-bution,” Appl. Opt. 42, 3009–3017 (2003).

14. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Un-wrapping (Wiley, 1998).

15. M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith,and C. J. Cogswell, “Linear phase imaging using differentialinterference contrast microscopy,” J. Microsc. (Oxford) 214,7–12 (2004).

16. F. Kagalwala and T. Kanade, “Reconstructing specimens usingDIC microscope images,” IEEE Trans. Syst. Man Cybern. B 33,728–737 (2003).

17. D. Biggs, AutoQuant Imaging, Inc., Troy, N.Y. 12180 (personalcommunication, 2005).

18. T. J. Holmes, S. Bhattacharyya, J. A. Cooper, D. Hanzel, V.Krishnamurthi, W. Lin, B. Roysam, D. H. Szarowski, and J.N. Turner, “Light microscopic images reconstructed by max-imum likelihood deconvolution,” in Handbook of BiologicalConfocal Microscopy, J. B. Pawley, ed. (Plenum, 1995), pp.389–402.

19. D. S. C. Biggs and M. Andrews, “Acceleration of iterative im-age restoration algorithms,” Appl. Opt. 36, 1766–1775 (1997).

20. Descriptions of Hamamatsu C5985 chilled CCD camera andHamamatsu C4742-95 high-resolution digital CCD camera areavailable at http://usa.hamamatsu.com.

21. The ImageJ software is available at http://rsb.info.nih.gov/ij/.22. The Mathematica software is available at http://www.

wolfram.com.23. A. Resnick, “Differential interference contrast microscopy as a

polarimetric instrument,,” Appl. Opt. 41, 38–45 (2002).24. R. Oldenbourg, S. Inoue, R. Tiberio, A. Stemmer, G. Mei, and

M. Skvarla, “Standard test targets for high resolution lightmicroscopy,” in Nanofabrication and Biosystems, H. C. Hoch,L. W. Jelinski, and H. G. Craighead, eds. (Cambridge U. Press,1996), pp. 123–138.


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Orientation-independent differential interference contrast … · OCIS codes: 180.0180, 100.2980, 170.1530, 170.3010, 170.3890, 170.3880. 1. Introduction Differential interference