1. Introduction

Optical contrast enhancement methods such as phase contrast, darkfield, differential interference contrast (DIC), spiral phase contrast (SPC), and others have been developed to increase the visibility of nearly transparent objects in optical microscopy. Many of these methods can be emulated by spatial light modulators (SLMs) [1]. Using the SLM, for instance, as a programmable Fourier filter has the advantage that switching between different modalities is fast and simple, as it can be performed by simply sending a different image to the SLM [2, 3]. SLMs acting as pure phase modulators inserted into a Fourier plane in the imaging pathway are often realized by miniaturized high resolution liquid crystal displays, typically with a pixel size of 10 µm x 10 µm and a display diagonal of 2 cm. This type of microscopic setup can be used for optical image processing [4, 5], aberration correction [6], and optical micromanipulation [7, 8].

In many respects it is advantageous to use the SLMs in an off-axis configuration, which means that the desired filter function is superposed on a blazed grating in the phase pattern on the SLM, such that the first order diffracted light of the blazed grating, which is spatially separated from the other diffraction orders by its different propagation direction, carries the processed image wave. A major advantage of this method is the fact that it suppresses the background of light unaffected by the SLM, which arises because of the imperfect diffraction efficiency of existing SLMs. Furthermore, in on-axis configuration a “phase-only” SLM can produce only a phase modulation of the wavefront, whereas in off-axis configuration the SLM can also act as an amplitude modulator, by spatially varying the local grating contrast (i.e. modulation depth) and thus the intensity of the diffracted light. Some techniques, such as darkfield imaging, require an off-axis configuration in the case of phase-only modulation, because of the necessary removal of the zero-order Fourier component of the incoming light, which would require an absorptive element in the on-axis variant [9, 10]. Furthermore, the capability to modulate the amplitude to a certain extent is also useful for modifying spiral phase contrast imaging [5] to create complex Laguerre-Gaussian filters [11], which obviously requires both amplitude and phase modulations.

Finally the wavefront modulation in the off-axis configuration is more precise than in the on-axis configuration in the sense that the latter suffers more from the restricted phase modulation capabilities of the SLM, related e.g. to nonlinearities in the phase shift of the SLM pixels, to the limited number of addressable phase levels, or to a restricted phase modulation range, which often falls below the nominal value of 2π. On the other hand, in off-axis operation the phase of the diffracted light field can be defined more accurately, since it is coded as the local spatial phase, i.e., the position, of a high resolution diffraction grating (similar to the situation in holography), in addition to the electronically addressed refractive indices of the liquid crystal pixels. Thus in off-axis mode it is possible to use an only binary SLM (e.g. a ferroelectric device) to program a continuous phase modulation of a diffracted wave [12].

Unfortunately the off-axis method also has disadvantages. One of these is the fact that the need to separate the first diffraction order from the other orders usually reduces the field of view, as will be discussed in more detail in the next section. Another disadvantage of the off-axis configuration is that it introduces dispersion in case of broadband or white light illumination, since the SLM grating diffracts different colors in the incoming wavelength range into different directions, corresponding to shifted image positions in the observation plane. Thus a white light image “smears out” by dispersion and sharp edges in the sample are displayed as rainbow-colored bars in the image. This is particularly disturbing for applications which rely on broadband illumination, such as microscopic imaging with ultra-short pulses, or Fourier filtering in optical coherence tomography [13]. Dispersion effects are also important when studying the chromatic effects that occur in the region of white-light optical vortices which were created by diffraction from a SLM. In this context it has been shown that the dispersion can be compensated by imaging the plane of the SLM onto a prism that introduces the opposite angular dispersion [14].

In previous work we have shown that the dispersion can be compensated by a double-pass technique [15], but in this approach only half of the SLM surface can be utilized for spatial filtering. In the following we introduce an easy-to-implement method where a blazed transmission grating made of glass is inserted into the optical pathway to obtain both the desired filter function and a sharp dispersion-free image for spectrally non-monochromatic (but spatially at least partially coherent) illumination without the need for splitting the SLM panel in half. And let us finally remark that recently a seemingly similar combination of a transmission grating and a SLM was also employed for quantitative phase imaging with white light illumination [16, 17], but in a different optical configuration where the grating was used as a beam splitter, not for dispersion compensation.

2. Experimental section

The experimental setup for realizing various SLM-based contrast enhancement methods in an optical microscope is sketched in Fig. 1 . For broadband sample illumination we either use a high power white light emitting diode (LZ4-00MD00, LedEngins Inc., 10 W), or a thermal light source (standard halogen bulb, 4.2 W). The light is coupled into a multimode acrylic fiber (0.4 mm core diameter) by using a focusing lens (L1, f₁ = 30 mm). The uniformly illuminated output of the fiber serves as the effective illumination source, defining the spatial coherence of the illumination light. Behind the fiber the beam is collimated by another lens (L2, f₂ = 30 mm) and illuminates the sample. The light transmitted through the sample is collected by a microscope objective (10 x magnification, air objective Reichert, Plan 10, NA = 0.2). A set of relay lenses (L3 and L4, with focal lengths of f₃ = f₄ = 200 mm) images the rear focal plane of the objective (corresponding to a Fourier plane of the optical path) on to the flat side of a ruled blazed glass transmission grating (30 x 30 x 10 mm, 17.5 lines / mm, blaze angle = 2.1°, Newport gratings).

 

Fig. 1 Schematic setup (not to scale) for the combination of a diffraction grating and a reflective SLM, the latter used as a Fourier filter in imaging, for avoiding dispersion effects due to white light illumination.

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A circular aperture is inserted between lenses L3 and L4 at the position of a sharp image plane, which reduces the field of view. This is necessary in order to limit the angular spread of the image wave in its Fourier plane ( = SLM plane) such that it is smaller than the diffraction angle at the displayed SLM grating. Without the aperture, different residual diffraction orders of the SLM (mainly the zeroth and the first order) would overlap in the camera plane, producing a disturbed image. Due to this restriction the usable field of view becomes

Behind the transmission grating the white light beam fans out into a “rainbow” with an angular range depending on the grating constant. Parts of the beam which are scattered into undesired diffraction orders (mainly into the zeroth order corresponding to undiffracted light) are spatially separated at some distance behind the grating, where they are blocked by a beam stop. The light field then passes through a relay system, consisting of two lenses (L5 and L6, f₅ = f₆ = 250 mm), to the surface of a reflective SLM (HOLOEYE Pluto). The relay system is adjusted such that it produces a sharp image of the transmission grating at the position of the SLM. Thus, also the SLM is located in a Fourier plane of the image field, and - at the same time - in a sharp image plane of the effective illumination source, namely the end face of the fiber.

By using achromatic lenses for the relay optics, the wave field in the SLM plane is not dispersed, and still corresponds to a spatial Fourier transform of the white light image wave. However, now each color within the wave field propagates into another direction. This dispersion is compensated by displaying a blazed phase grating at the SLM which back-diffracts the incoming beam into its original travelling direction (i.e. the direction the beam would have if no gratings, just mirrors and lenses, were in the beam path).

Since the SLM is reflective, this would mean a back-diffraction to the position of the transmissive grating. Therefore, in order to separate the beams, the SLM is slightly tilted (10°), such that the wave is diffracted away from the original optical axis to the camera plane. Note that in the more general case of a relay lens system with a non-unity magnification factor, for optimal dispersion compensation the blazed phase grating displayed at the SLM has to be a phase conjugate copy of the image of the transmission grating in the SLM plane. This means that behind the SLM the sum of the phase modulations produced by the first phase grating, and by the SLM grating, is again spatially flat, and therefore the total diffraction angle is the same for all colors in the beam. The blazed grating displayed at the SLM can be experimentally adjusted such that the incoming “rainbow-beam” is optimally recombined into a white light beam, which then travels through an imaging lens (which performs a Fourier back-transformation, L7, f₇ = 200 mm) into the observation plane where a camera chip is located (Canon EOS 1000D).

The procedure for adjusting the dispersion compensation is demonstrated in Fig. 2 . First, the transmission grating is removed from the optical setup, and the SLM is programmed to act as a plane mirror, by setting the phase value of each pixel to zero. Since in this case no diffractive structures are present in the beam path, the image of a test sample (part of a resolution target) can be recorded without dispersion in the center of the camera chip (Fig. 2(A), arrow). The circular shape of the image is due to the aperture between lenses L3 and L4 which reduces the field of view in order to prevent different diffraction orders from overlapping. In the next step, the blazed glass grating is reinserted into the beam path, which results in an efficient diffraction of the incoming beam into one diffraction order. This leads to both, a lateral shift of the image in the camera plane and dispersion of the white light into a fan of rainbow colors (Fig. 2(B), arrow). A blazed phase grating is then displayed on the SLM, with a grating constant which is experimentally optimized to compensate for the diffraction effect of the glass transmission grating. This is achieved, when the image of the double diffracted wave is located again at its original position (as in Fig. 2(A)) in the center of the CCD frame (Fig. 2(D), arrow). Note that in this case also the dispersion is compensated, i.e. the central image of the resolution target does not show any dispersion effects. The only difference to the undiffracted image in Fig. 2(A) is that its color has shifted towards the red. This is due to the wavelength dependence of the diffraction efficiencies at the two gratings, which is in total higher in the red regime. However, this does not introduce any dispersion blurring in the picture. For demonstrating the effect of the pure SLM grating, Fig. 2(C) shows an image where the SLM grating is displayed without the transmissive glass grating in the beam path. In this case the image is again displaced from the center of the CCD chip, however now into the opposite direction as before (Fig. 2(C), arrow). Consequently, also the direction of the color blurring is flipped with respect to Fig. 2(B). Thus it is seen that the effect of any of the two gratings can be compensated by the other.

 

Fig. 2 Method for adjusting the dispersion compensation in four steps. (A): sample without any gratings (brightfield), (B): the blazed glass grating is inserted in the optical pathway and causes diffraction of the incoming beam, (C): a grating is displayed on the SLM (grating is phase conjugated to the blazed glass grating), (D): the combination of the glass grating and the SLM leads to a dispersion free image which is at its original position.

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Here it has to be noted that, in fact, not the first order diffraction of the glass transmission grating (grating period: 58 µm) was used for imaging, but instead the second diffraction order, since this provided the maximal diffraction efficiency in the used wavelength range. Consequently, for compensation the SLM grating (which acted in first diffraction order) was programmed with a doubled line frequency (grating period: 28 µm) for producing the required back-diffraction angle. This has no disturbing effect on the dispersion compensation, as long as the actual diffraction angles of both gratings are the same.

After this kind of adjustment, the SLM phase masks for various image processing applications can be computed as if they were designed for on-axis operation, and then numerically added to the previously optimized blazed grating phase, followed by a modulo 2 π operation. This final modulo 2 π operation of the actual filter mask superposed on the blazed grating assures a fixed “linkage” between the two diffractive structures, i.e. all light diffracted into the first diffraction order of the blazed grating is also “automatically” filtered by the programmed phase mask - independent of the detailed SLM characteristics. For example, a limited phase modulation range of the SLM would affect in this case only the efficiency, but not the precision of the programmed wave front in the first diffraction order.

3. Experimental results

The method described above was tested using both, amplitude and phase objects as specimen for different Fourier contrast enhancing methods, namely darkfield, phase contrast and spiral phase contrast microscopy. The results are shown in Fig. 3 .

 

Fig. 3 First row shows the images of a resolution target as an amplitude object, the 2nd and 3rd row show onion epidermal cells and human epithelial cheek cells as phase objects. The insets on the very top of row show the corresponding phase patterns displayed on the SLM. Image illumination was performed with a white light LED.

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As an absorptive test object with amplitude contrast (upper row A in Fig. 3) we employed a section from a USAF Glass Slide Resolution Targets (Edmund Optics). In the images the brighter parts correspond to transmissive regions of the sample, whereas the dark parts are absorbing bars. For comparison the first column (from the left) shows an image recorded without diffractive structures in the beam path i.e. the glass grating was removed and the SLM was used as a mirror (zero diffraction order). The corresponding phase masks, displayed on the SLM, are sketched at the very top of row A (not to scale). The next image shows the same section of the sample with both gratings activated, after performing the primary adjustment described before. This imaging modality corresponds to a brightfield image in standard microscopy, although now the image wave is doubly diffracted at two gratings. The “reddish” appearance of the image is due to the characteristics of the diffraction efficiencies of the two gratings, which are most efficient in the red wavelength regime. Images corresponding to other diffraction orders are dimly visible above and below the central image, demonstrating the necessity to restrict the field of view with an aperture in order to prevent overlapping of the diffraction orders.

The next column shows the result of an off-axis spiral phase filter displayed on the SLM. As expected, the edges within the sample are isotropically highlighted, without observable dispersion-induced blurring. The next column shows the result of darkfield operation, which is only possible in off-axis operation of the (phase-only) SLM, since it requires removal of the zero Fourier component of the image wave, which is located in the center of the filtering region. There, the zero-order Fourier component (corresponding to the sharp image of the illumination source - namely the output face of the illumination fiber, without inserted sample) is removed by “cutting out” a circular area in the center of the phase grating displayed on the SLM: Since only light diffracted at the SLM grating travels to the camera plane, the omission of the grating at certain regions in the SLM plane removes the respective Fourier components. Similar to the spiral phase filtered image, only the edges of the sample are highlighted, however, with a strongly reduced intensity.

Finally, the image in the last column shows the result of a central phase contrast filter (in off-axis mode) displayed at the SLM. There, a circular area in the center of the SLM surface (where again the zero Fourier component of the image wave is located) contains a phase grating with a shift of its spatial phase by π/2, as compared to the surrounding diffraction grating (see bottom row). This spatial shift of the grating phase is imprinted on the diffracted light, such that the zero Fourier component of the image is shifted also by π/2 with respect to the other components - which is the condition for obtaining a phase contrast image. However, as expected, such a phase contrast operation does not improve the contrast for the absorptive test sample (in fact, it even transforms the amplitude contrast partially to a phase contrast, thus strongly reducing the final image contrast). As shown later for the phase samples below (Fig. 3, row B and C), the usefulness of phase contrast imaging emerges when investigating thin phase samples.

The next two rows (B and C) in the figure show the results of the above described Fourier filtering operations applied to phase samples, namely a section of onion epidermal cells (row B) and human cheek cells (row C), each unstained and individually sandwiched between two coverslips in a watery environment. Notably, the use of the filtering operations is most pronounced for the case of the optically very thin cheek cells. There, cell boundaries and the cell cores are not visible in brightfield operation (first and second columns), dimly accentuated in darkfield mode (fourth column) and clearly highlighted in spiral phase contrast and central phase contrast (third and fourth rows, respectively). Because of white light illumination, the images are free from speckle artifacts (which would occur for narrowband laser illumination), and at the same time, in spite of the broadband illumination, free from obvious dispersion effects, as there are no colored edges.

As a further example for off-axis filtering, Figs. 4(A-C) show images obtained with spiral phase contrast filters displaced by a small amount with respect to the optical axis to create a pseudo-relief effect, namely displaced to the top, Fig. 4(A), centered, Fig. 4(B), and displaced to the bottom, Fig. 4(C). Whereas the centered filter, Fig. 4(B), produces an image with isotropic edge enhancement, the displacements in Fig. 4(A) and Fig. 4(C) produce a kind of “shadow” or “pseudo-relief” effect, i.e., the obtained images give the impression of a topographically structured surface which is illuminated from different directions. This kind of shadow-effect resembles the appearance of samples in DIC, and helps the observer to gain a topographic view of the “landscape” of a specimen, for example for distinguishing elevations from depressions in phase samples. Furthermore it has been already shown that a set of images recorded with different apparent illumination directions enables the interferometric reconstruction of complex samples [15]. The series of images also indicates one advantage of SLM-based image filtering, namely that switching between the different views can be performed purely electronically, and at video rate (refresh rate of the current SLM is 60 Hz). Again, this method can now be extended to operate also with broadband illumination.

 

Fig. 4 Pseudo-relief structures of a resolution target, recorded with a white light LED illumination sorce. It seems that the object is illuminated from three different directions. These shadow-effect images are obtained by filtering with spiral phase holograms on the SLM.

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4. Conclusions and outlook

We have demonstrated a method to compensate for undesired dispersion effects in SLM-based Fourier filtering microscopy, by implementing a static diffraction grating in the optical path. This allows one to use a multitude of recently developed SLM Fourier filtering applications with standard microscopic illumination, instead of the currently employed narrowband illumination sources. The method is insensitive to slight misalignment of the transmission grating and does not require any additional high prized components. Thus it should be useful for extending the range of applications for SLMs in microscopy. Using optimized blazed gratings for this purpose, the light efficiency of standard microscopy is not reduced.

Similar advantages may be gained for SLM-based light projection [18, 19], for beam steering of optical tweezers, or for display technology. In each case, it is again desirable to program the diffractive structures as off-axis masks, due to the arguments mentioned above (such as the suppression of the background of undiffracted light, the option for amplitude modulation via the local modulation depth in the grating structure, and less sensitivity to imperfections of the SLM). However, off-axis operation also limits the projection systems to narrowband light due to dispersion effects. A similar pre-dispersion method with a static grating as demonstrated here is essential for white light projectors or for illumination by ultra-short pulses.