2.1.

Optical Scheme of Microscope for Combined Orientation-Independent DIC and Polarization Imaging

A regular research-grade microscope equipped with DIC prisms, polarization state generator (or compensator), circular analyzer, and precision rotatable stage can be employed for obtaining orientation-independent DIC (OI-DIC) and polarization images. Figure 1 illustrates the optical setup that we used. The setup was implemented on an upright microscope Microphot SA (Nikon, Melville, New York, http://www.nikoninstruments.com). The microscope consists of a light source Sc, bandpass filter F, condenser and objective lenses C and O correspondingly, rotatable stage RS, a pair of removable Nomarski prisms DIC1 and DIC2, left circular analyzer, and CCD camera Retiga EXi Fast (QImaging, Surrey, British Columbia, Canada, http://www.qimaging.com), which is connected to a computer. Sp is a specimen under investigation. As a light source, we used a high-pressure mercury arc lamp followed by an Ellis fiber-optic light scrambler (Technical Video, Port Townsend, Washington, http://www.technicalvideo.com). The bandpass interference filter with central wavelength $546\mathrm{nm}$ and 30-nm full width at half maximum (Chroma Technology, Rockingham, Vermont, http://www.chroma.com) selected the bright green mercury line for illumination.

Fig. 1

Scheme of a microscope setup for combined orientation-independent DIC and polarization imaging: Sc, light source; F, bandpass filter; P $\left(45\mathrm{deg}\right)$ , polarizer at 45-deg azimuth; LCA $(\alpha ,90\mathrm{deg})$ and LCB $(\beta ,45\mathrm{deg})$ , liquid crystal variable retarders with retardances $\alpha$ and $\beta$ at azimuths $90\mathrm{deg}$ and $45\mathrm{deg}$ correspondingly; DIC1 $\left(0\mathrm{deg}\right)$ and DIC2 ( $0\mathrm{deg}$ , $\Gamma$ ), removable Nomarski prisms at 0-deg azimuth (the second prism introduces bias $\Gamma$ ); C, condenser lens; RS $\left(\sigma \right)$ , rotatable stage at azimuth $\sigma$ ; Sp, specimen under investigation; O, objective lens; QWP $\left(0\mathrm{deg}\right)$ , quarter-wave plate at azimuth $0\mathrm{deg}$ ; A $\left(45\mathrm{deg}\right)$ , linear analyzer at azimuth $45\mathrm{deg}$ ; CCD, imaging detector (CCD camera); XYZ, Cartesian coordinate system. The linear polarizer and two variable retarders form a complete polarization state generator (PSG). The quarter-wave plate and linear analyzer form a left circular analyzer.

For description of the setup, we use the right-handed Cartesian coordinate system $xyz$ . The $z$ axis is parallel to the microscope axis toward the beam propagation. The $x$ axis is parallel to the shear direction of the prism DIC1. The orientations of the retarders in the $x$ - $y$ plane are defined by their slow axis. The orientations of the linear polars are determined by their electric vector transmittance axis. The angle is positive if measured counterclockwise and negative if measured clockwise from the $x$ axis, when one is looking “into the beam.”

Two liquid crystal variable retarders LCA and LCB together with linear polarizer P (CRi, Inc., Woburn, Massachusetts, http://www.cri-inc.com) form a complete polarization state generator (PSG),⁵ which is also called a universal compensator.⁶ The polarizer P is oriented at $45\mathrm{deg}$ . The variable retarders LCA and LCB are oriented at $90\mathrm{deg}$ and $45\mathrm{deg}$ , accordingly. This arrangement, which can produce any light polarization, was proposed by Yamaguchi and Hasunuma in 1967.^{7, 8} The variable retarders LCA and LCB introduce retardances $\alpha$ and $\beta$ , correspondingly. The basic setting of the retarders is $\alpha =90\mathrm{deg}$ and $\beta =180\mathrm{deg}$ . In this case, the PSG creates a right circular polarized beam, where the $E_x$ component leaves behind the $E_y$ component on $\lambda ∕4$ distance, where $\lambda$ is wavelength. The quarter-wave plate QWP with orientation $0\mathrm{deg}$ and linear analyzer A with orientation $45\mathrm{deg}$ construct a left circular analyzer. We used a left circular analyzer made of a laminated polymer achromatic wave plate and polarization film (Bolder Vision Optics, Boulder, Colorado, http://www.boldervision.com).

The complete polarization state generator (PSG), left or right circular analyzer, and CCD camera with computer are employed for obtaining images of 2-D birefringence distribution.^{6, 9} It is possible also to use other kinds of PSG, such as rotatable elliptical polarizer,¹⁰ rotatable linear polarizer,¹¹ or combination of liquid crystal variable retarders LCA and LCB with orientation angles $22.5\mathrm{deg}$ and $67.5\mathrm{deg}$ ,¹² etc. The prisms DIC1 and DIC2 are taken out during the capturing of raw polarization images. A brief description of algorithms for obtaining orientation-independent polarization images is given in Sec. 2.3.

In order to switch to the DIC mode, the prisms must be moved back into the beam, as shown in Fig. 1. The polarization state generator is in the basic setting to create the right circular polarized illumination beam.

The prism DIC1 splits the input beam angularly along the $x$ axis into two orthogonally polarized beams with components $E_x$ and $E_y$ . The axis of the first beam with component $E_x$ is parallel to the $z$ axis. The second beam is deviated on a small angle ${\epsilon }_1$ . The component intensities are the same, but there is a quarter-wave optical path difference $\lambda ∕4$ between them because the input beam is circularly polarized. The condenser C makes the beam axes parallel with a small shear $d$ . Then the objective lens O joins the beam axes in the back focal plane. The second prism DIC2 introduces an opposite small angular deviation ${\epsilon }_2$ into the second beam with component $E_x$ . The angles ${\epsilon }_1$ and ${\epsilon }_2$ are connected with the focal distances of the condenser and objective lenses $f_c$ and $f_{ob}$ and the shear amount $d$ by the following formula:

We captured two pairs of regular DIC images at orientations of the stage $\sigma =0\mathrm{deg}$ and $\sigma =90\mathrm{deg}$ . In each pair, the images were taken with small biases having the same magnitude and opposite signs. The computer then rotated off-line the second image pair on $-90\mathrm{deg}$ and aligned one with the first image pair. The four images are processed further to get the OI-DIC image. The corresponding processing algorithm is briefly described in the next section.

2.2.

Algorithm for Orientation-Independent DIC Imaging

Recently, we proposed a DIC microscopy technique that records phase gradients within microscopic specimens independently of their orientation.^{13, 14} For description of the specimen under investigation, we use a local Cartesian coordinate system $x^{\prime }{y}^{\prime }$ , which is connected with the rotatable stage RS. If the stage orientation $\sigma =0\mathrm{deg}$ , then the $x^{\prime }$ axis coincides with the $x$ axis of the main coordinate system. In case of $\sigma =90\mathrm{deg}$ , the $y^{\prime }$ axis coincides with the $x$ axis. A DIC image can be modeled as the superposition of one image over an identical copy that is displaced along the $x$ axis by a shear amount $d$ and phase shifted by bias $\Gamma$ . The intensity distribution in the DIC image $I^{DIC}(x^{\prime },y^{\prime })$ can be described by the following formula:

Here, we assume that the intensity of each interfering imaging beam after the analyzer A equals $\frac{1}{4}$ of intensity $\tilde{I}(x,y)$ , retardance of the specimen and depolarization caused by the optical components are small and can be neglected, polarizer P and analyzer A are ideal, and the ambient light is absent.

If the product $d\gamma$ is small $(d\gamma ⪡\lambda ∕2\pi )$ , Eq. 2 can be reduced to sum of two terms:

Then the camera captures an image pair of the rotated specimen $I_3^{DIC}(-y,x)$ and $I_4^{DIC}(-y,x)$ at $\sigma =90\mathrm{deg}$ . After, the computer rotates digitally the second image pair on $-90\mathrm{deg}$ to get the same orientation for all images:

The following two equations calculate the gradient magnitude and azimuth distribution of the optical paths in the specimen:

Also, after computing the optical path gradient distribution, enhanced regular DIC images can be restored with any shear direction.¹⁴ The enhanced image provides a calculated image for any desired shear direction and bias without the requirement to directly collect an image for that shear direction and bias. Moreover, the enhanced image will have less noise than a regular DIC image, and it suppresses deterioration of the image due to specimen absorption and illumination nonuniformity.

Optical phase $\Phi (x,y)$ shows the dry mass distribution of a specimen and can be obtained by computing a line integral.^{14, 15} Also other techniques for phase computation can be used, for instance, iterative computation,¹⁶ noniterative Fourier phase integration,¹⁷ or nonlinear optimization with hierarchical representation,¹⁸ etc. Biggs has developed an iterative deconvolution approach for computation of phase images, based on the same principles as deconvolution techniques normally used to remove out-of-focus haze.¹⁹ When processing DIC data, the point spread function (PSF or $h$ ) that describes the image formation process can be approximated¹⁶ using a positive and negative Dirac delta $\delta$ function separated by the shear distance $d$ :

The processing is assumed to operate on the differential phase data, which can be calculated from the intensity images taken at the shear orientations with 90-deg differences:

Using Eqs. 3, 4, we can derive the following equations for the differential phase data $OP{D}_0(x,y)$ and $OP{D}_{90}(x,y)$ :

The two resulting data sets have orthogonal shear directions (and orthogonal PSFs) but a common underlying phase object. As mentioned earlier, any absorption variations have been eliminated by calculating the ratios of image intensities. The observed differential phase is simply the true object $\Phi (x,y)$ convolved $(\otimes )$ with the PSF, plus a noise component $n(x,y)$ :

2.3.

Algorithm for Orientation-Independent Polarization Imaging

In order to switch to the Pol (polarization) mode, the prisms must to be moved out from the beam. The rotatable stage RS is oriented at $\sigma =0\mathrm{deg}$ . Thus, the specimen coordinate system $x^{\prime }{y}^{\prime }$ is coincident with the microscope coordinate system $xy$ . For obtaining orientation-independent polarization images, we employed the four-frame algorithm proposed by Shribak.^{10, 21} The algorithm computes 2-D distributions of retardance $\Delta (x,y)$ and slow-axis orientation (azimuth) $\phi (x,y)$ of the specimen under investigation.

Intensity distribution in a Pol image $I^{Pol}(x,y)$ , which is created after the left circular analyzer, can be described by the following formula:

At first, we record an image pair $I_1^{Pol}(x,y)$ and $I_2^{Pol}(x,y)$ with negative and positive small bias $\chi$ applied to nominal retardance of the first variable retarder ( ${\chi }_{\alpha }=\mp \chi$ , ${\chi }_{\beta }=0\mathrm{deg}$ ):

Usually, we have $\Delta ⪡\chi$ . In this case, the formula for computation of the specimen retardance can be simplified as:

3.1.

OI-DIC Images of Human Cheek Squamous Epithelial Cells

Human cheek cells are excellent transparent test specimens commonly used for alignment of the microscope for phase contrast and DIC.^{2, 22} For the preparations used here, a buccal smear of cheek cells was dispersed in a drop of $1\times$ phosphate-buffered saline (Sigma-Aldrich, St. Louis, Missouri, http://www.sigmaaldrich.com) on a 1.5-thick coverslip, which was then inverted onto a clean slide and pressed down to spread the cells into a thin layer. Four conventional DIC images were obtained, as explained in Sec. 2.1. We used the Nikon Microphot-SA microscope equipped with a $20\times ∕0.5$ Plan DIC objective lens. Bias of 1/15 wavelength was introduced with a Brace-Koehler compensator.

Figure 2 (left) illustrates one of the captured conventional DIC images. Figure 2 (center) is a grayscale image of gradient magnitude computed from Eq. 5. Here, brightness is linearly proportional to the magnitude. The gradient magnitude image clearly shows the cell and nuclear boundaries independently of orientation. The computed phase is entirely consistent with the structure seen with conventional DIC, but the clarity is significantly improved. Notice also how the large ( $10\text{-}\mu \mathrm{m}$ diam) optically refractive nucleus appears distinct within the cheek cell cytoplasm in this image.

Fig. 2

Conventional and computed orientation-independent DIC images of human cheek squamous epithelial cell.

3.2.

Orientation-Independent DIC Images of Sciara coprophila Polytene X Chromosomes

Application of OI-DIC to isolated chromosomes is illustrated using giant salivary gland chromosomes from the fungus gnat, Sciara coprophila. Salivary glands were obtained from female larvae in Robert’s CR medium ( $87\mathrm{mM}\mathrm{NaCl}$ , $3.2\mathrm{mM}\mathrm{KCl}$ , $1.3\mathrm{mM}{\mathrm{CaCl}}_2$ , $1\mathrm{mM}{\mathrm{MgCl}}_2$ , $10\mathrm{mM}\mathrm{Tris}\text{-}\mathrm{HCl}$ ; pH 7.3) and gently squashed on a coverslip to spread the chromosomes.

Figure 3 shows how the banded appearance of these polytene chromosomes (which result from the recombination and repeated replication of chromosomal DNA) can be imaged in both conventional DIC and gradient magnitude modes. Sites where chromosomal DNA is dispersed (“puffs”) are clearly evident. These images were obtained under the same experimental conditions as for the human check cells described in the preceding section, except for microscope lens NA. Here, we used a $40\times ∕0.7$ Plan DIC objective.

Fig. 3

Conventional and computed orientation-independent DIC images of Sciara polytene X chromosomes.

3.3.

OI-DIC Images of Vorticella

Here, experimental results with biological specimens explored at very high image resolution are presented. The protist Vorticella convallaria is especially interesting, as its spasmoneme is among the fastest and most powerful cellular engines known.²³ Figure 4 shows conventional DIC, gradient magnitude, and phase images of an anesthetized Vorticella cell with a contracted stalk. The cell was induced to contract by the addition of dibucaine hydrochloride D0638 (Sigma-Aldrich, St. Louis, Missouri, http://www.sigmaaldrich.com), a local anesthetic that demonstrates many other cellular effects secondary to its anesthetic capabilities. In order to obtain the OI-DIC images, four conventional DIC images were made, as described earlier. The images were then digitally aligned and processed to obtain those displayed in the center and right panels of Fig. 4. The setup was a Nikon Microphot-SA microscope equipped with a $60\times ∕1.4\mathrm{NA}$ oil immersion objective lens and a Universal Achromatic-Aplanat condenser with the same NA at wavelength $546\mathrm{nm}$ .

Fig. 4

Conventional DIC image and computed orientation-independent DIC images of Vorticella.

In the phase image, the vacuoles (with their lower dry mass) clearly stand out from organelles with higher optical density. The spasmoneme has obviously contracted within the stalk, as seen by its increased concentration away from the cell body. The contracted spasmoneme is $4.3\text{-}\mu \mathrm{m}$ thick, and it tightly fills the sheath. Also some of the structures within the oral groove—the basal bodies near the “mouth” of the cell (farthest from the stalk connection) and cilia (within the middle-left portion of the cell body)—stand out distinctly. Many detached cilia are evident floating in the area surrounding the cell, apparently detached from the cell in response to the dibucaine treatment used to anesthetize the cell.

Deserving emphasis is the fact that images with such high fidelity and resolution, and reflecting the true distribution of optical paths (dry mass), cannot be obtained with conventional phase contrast or interference contrast techniques. The former introduces a halo around regions with high optical path differences in the specimen, by suppressing low-frequency details because of spatial filtration by the phase annulus. Interference microscopy, on the other hand, cannot be used with high NA lenses, thus preventing the achievement of high image resolution. Our new approach improves upon the resolution, image quality, and fidelity of DIC, phase contrast, and interference microscopy and finally allows acquisition of images that depict the true optical path difference at the highest resolution of well-corrected microscope lenses. These results demonstrate that the proposed DIC technique can successfully image and measure phase gradients of transparent specimens, such as those of biomedical interest, independent of the directions of the gradient, and minimally influenced by specimen absorption.

3.4.

Comparison of OI-DIC, Phase Contrast, and Interference Images of Fixed Bovine Pulmonary Artery Endothelial Cells

Our first attempts at imaging a biological specimen with the OI-DIC technique were done using a specimen slide containing fixed and stained bovine pulmonary artery endothelial cells that are commercially available from Invitrogen (Carlsbad, California, slide product number F14780). These cells were chosen because of their distinct shape. In an earlier report,¹⁴ we described the improvements made by OI-DIC in the imaging of these cells in comparison to images made with conventional DIC. Here, we present results obtained with phase contrast and interferometric microscopy techniques.

Figure 5 demonstrates a phase image obtained with OI-DIC technique (left), a conventional phase contrast image (center), and an interference image of the cell (right). The images show the dry mass distribution of the cell under investigation.

Fig. 5

Computed OI-DIC image positive phase contrast image, and interference image of bovine pulmonary artery endothelial cell.

In order to obtain the OI-DIC image, we employed a Nikon $20\times ∕0.75\mathrm{NA}$ objective and a Nikon Universal Achromatic-Aplanat $1.4\mathrm{NA}$ condenser stopped down to match the objective NA. Four conventional DIC images were collected and aligned as described earlier. Then the phase image was computed via iterative deconvolution. The OI-DIC phase images clearly reveal the refractive boundaries and detailed structures of the cell. The image brightness is linearly proportional to the dry mass.

The phase contrast image was obtained with a Nikon Microphot-SA microscope equipped with an ePlan $40\times ∕0.65$ phase objective lens containing a positive phase ring. With this phase ring, specimens having a higher refractive index than the surrounding medium appear dark on a neutral gray background, while those specimens that have a lower refractive index than the bathing medium appear brighter than the gray background. The phase image has two artifacts:

The interference image was obtained with a Jamin-Lebedeff microscope equipped with a Pol-Int II $40\times ∕0.65$ objective lens and a Senarmont compensator. The objective lens introduces $180\text{-}\mu \mathrm{m}$ displacement between the probe and reference beams in the object plane. The specimen under investigation does not have an empty space around the cell for the reference beam. Therefore, the interference image contains blurred areas from the surrounding structure. The image brightness depends on the dry mass nonlinearly.