2.1. Drawbacks of conventional viability estimations

As pollination is the primary function of the pollen grain in a plant life cycle, one way to test pollen viability is to use the pollen for pollination and subsequently analyse the seed set. However, this is time-consuming and often not feasible; thus, other methods are frequently used to elucidate pollen viability, such as staining techniques, in vitro or in-vivo germination, as well as semi-in situ germination on the excised stigma (stigmatic germination), or impedance flow (IF) cytometry, but again, most of these are difficult to scale up and further confounded by incompatibilities, post-fertilisation barriers and limited measurability, factors that restrict the accuracy of these tests (Dafni & Firmage, Reference Dafni and Firmage2000; Dionne & Spicer, Reference Dionne and Spicer1958).

Vital staining is by far the fastest and most commonly used method of pollen viability estimation, but the last major advance in this area was almost half a century back when the Heslop-Harrisons developed a viability test based on fluoro-chromatic reaction-based membrane integrity and enzyme activity (Heslop-Harrison, Reference Heslop-Harrison1977; J. Heslop-Harrison & Heslop-Harrison, Reference Heslop-Harrison and Heslop-Harrison1970; Shivanna & Heslop-Harrison, Reference Shivanna and Heslop-Harrison1981). In general, pollen staining involves visualisation of specific compounds, contents or cellular compartments that take up the dye colour, while the absence of colour indicates aborted pollen (Stanley & Linskens, Reference Stanley and Linskens1974; Alexander, Reference Alexander1969). Confounding factors in this procedure include failures to discriminate different viability levels, the toxicity of dyes being a concern for human health apart from the dye stain rendering pollen grains unfit for germination (Ge et al., Reference Ge, Fu, Bhandari, Bouton, Brummer and Wang2011). Refined viability estimations have been attempted by comparing and combining techniques like cytometry and staining in case of mature cucumber, sweet pepper and tomato pollen (Heidmann et al., Reference Heidmann, Schade-Kampmann, Lambalk, Ottiger and Di Berardino2016). However, pollen viability assessment purely through microscopy, as envisaged in this work, has not been investigated up till now.

2.2. Imaging of pollen grains and limitations of current methods

Traditionally, palynologists have used compound light microscopy for pollen identification and interpretation and scanning electron microscopy (SEM) for morphological comparisons and taxonomy (Jones & Bryant, Jr., Reference Jones and Bryant2007). Doubtless, SEM offers far greater resolution, but sample preparation and the time needed to count, analyse, photograph and print the micrographs, and the consequent lack of scalability are the limiting factors. Flow cytometry methods were then described to determine pollen viability based on the nuclear DNA content in mature pollen grains, but this is a fairly lengthy and expensive process not suitable for a quick estimate (Bino et al., Reference Bino, Tuyl and De Vries1990).

With the advancement of digital microscopy, palynology studies are becoming less time-consuming and can generate more reliable data for species taxonomy, apart from saving hours spent on manual counts of pollen grains following the process of staining to differentiate between viable and non-viable pollen (S. Mishra & Srivastava, Reference Mishra and Srivastava2015). At the turn of the millennium, alternative digital methods for counting pollen were devised, but often without regard to viable and non-viable grains, and these protocols also had drawbacks of software specific to branded instruments (Aronne et al., Reference Aronne, Cavuoto and Eduardo2001; Bechar et al., Reference Bechar, Gan-Mor, Vaknin, Shmulevich, Ronen and Eisikowitch1997). More recently, particle counters and binary 2D projection, including shape-based Fourier descriptors and topological features, have been used, but the success varies by species, and is applicable only when size difference settings for viable and non-viable grains is larger than the natural variation in viable pollen size for that species (Akcam & Lohweg, Reference Akcam and Lohweg2022; Kelly et al., Reference Kelly, Rasch and Kalisz2002; Mudd & Arathi, Reference Mudd and Arathi2012).

In summary, digital image processing appears to overcome size-based differences and species limitations but has not been explored sufficiently widely, emphasising the importance of another simpler method for pollen gain imaging in natural/hydrated state for assessing viability, as described in this work by means of the DHM imaging methodology.

2.3. Digital holographic microscopy for pollen imaging

DHM is an interferometric imaging modality that uses a low-power (few milliwatts) coherent laser illumination in a Mach–Zehnder configuration. As shown in Figure 1a,b, the laser beam is first split in two. One of the beams is transmitted through the pollen sample and forms the image field $O(x,y)$ at the detector plane, while a second beam takes an identical path without any sample and forms a tilted plane reference $R(x,y)$ . Since the two optical fields $O(x,y)$ and $R(x,y)$ have originated from the same coherent laser beam and travel near identical path lengths up to the detector, they are temporally coherent and produce interference fringes with good contrast at the detector. A low-power light source is sufficient for this modality as we are not exciting any fluorescence labels but simply transmitting the light beam through a semi or fully transparent sample. The interference pattern (or digital hologram) $H(x,y)$ recorded on the pixelated array detector may be mathematically described by

(1) $$ \begin{align} H(x,y) &= \lvert R(x,y) + O(x,y) \rvert^2 \nonumber \\&= \lvert R \rvert^2 + \lvert O \rvert^2 + R^*O + RO^*. \end{align} $$

The * operation above is a complex conjugation of wave functions associated with the object and reference beams. Our DHM system implements image plane holography, where $O(x,y)$ represents the image field of the pollen recorded using a 40 $\times $ infinity-corrected imaging system. The image field $O(x,y)$ at the detector plane is a complex wave function and contains both amplitude and phase parts. The amplitude part signifies the information regarding the attenuation or absorption of the illuminating light when passed through the pollen sample. The important feature of a DHM is that it is able to record and numerically reconstruct the phase $\phi (x,y)$ of the image field as well. The phase map $\phi (x,y)$ may be interpreted physically as a projection:

(2) $$ \begin{align} \phi(x,y) = \frac{2\pi}{\lambda} \int n(x,y,z)\ dz. \end{align} $$

Here, $n(x,y,z)$ represents the relative refractive index in the 3D space of the pollen sample relative to the surrounding medium. In other words, the phase function $\phi (x,y)$ represents the optical path length for the illuminating laser beam through the sample pollen. Note that the refractive index $n(x,y,z)$ is an inherent material property of the pollen grain being imaged. This material property is thus recoverable from a DHM system but not accessible with a bright-field system. Note that the refractive index $n(x,y,z)$ has been integrated over the depth of the sample (or the propagation direction z of the laser beam through the sample). For completeness, we remark that the more commonly used phase contrast mode in microscopes does utilise the phase property of light to enhance the qualitative visual appearance of the samples. We have provided comparative images of two pollen grains in bright-field, phase contrast and quantitative phase modes in Supplementary Figure S1. This supplementary illustration suggests that unlike DHM imaging, the traditional phase contrast information is qualitative in nature and does not bring out distinct morphological features of viable versus non-viable pollen.

Figure 1. Digital holographic microscope system used in the present study. (a) System photograph. (b) Nominal optical layout of the system. $B_1, B_2, B_3$ : beam-splitters; M: plane mirror. The beam-splitter $B_3$ can be rotated with an adjustable screw in order to introduce tilt in the reference wave as required for off-axis hologram recording. The system is fitted with a laser source for phase imaging and LED illumination with condenser for bright-field illumination. By switching between the two illuminations, one can record an image plane digital hologram or a bright-field image of the sample in the same position.

We highlight here that DHM is a computational microscope. The phase information of interest is not directly measured on the array detector. Phase can, however, be estimated computationally using numerical processing of the recorded hologram pattern $H(x,y)$ at the detector plane. The speciality of our DHM system is that it provides single-shot phase imaging at full diffraction limited resolution. With current advances in the CMOS array sensor technology, a good contrast fringe pattern may be recorded in just a millisecond exposure time when used with a few-milliwatt laser source for illumination as in our case. The single-shot operation is advantageous as the system is not very sensitive to the surrounding vibrations during the exposure time.

Single-shot off-axis holograms as in our study are conventionally reconstructed using the Fourier-transform method (Kreis, Reference Kreis1986; Takeda et al., Reference Takeda, Ina and Kobayashi1982). This method inherently involves a low-pass filtering operation and, as a result, the recovered object wave function $O(x,y)$ often has lower resolution compared with the diffraction-limit of the infinity corrected imaging system used. In image plane holography, this loss of information results in blurring of edges in the image field that are critical to perception of image quality. Contrary to this, the bright-field images recorded using the same infinity corrected imaging system allow full diffraction-limited resolution. Hence, the phase information recovered using the Fourier-transform method has lower spatial resolution compared with the conventional bright-field images. Other methods such as phase-shifting methods (Creath, Reference Creath1988; Yamaguchi, Reference Yamaguchi2006) can deliver the expected full resolution, but require multiple hologram recording with much stringent vibration isolation, making the DHM system costs high. In order to retrieve the phase information with full pixel resolution from a single-shot off-axis hologram, we use a sparse optimisation method that we developed over last several years of effort (Khare et al., Reference Khare, Ali and Joseph2013; Mangal et al., Reference Mangal, Monga, Mathur, Dinda, Joseph, Ahlawat and Khare2019; Singh & Khare, Reference Singh and Khare2017, Reference Singh and Khare2018). The resolution and phase accuracy advantages (Singh et al., Reference Singh, Khare, Jha, Prabhakar and Singh2015) of this optimisation method are already well established in prior literature.

In brief, in the sparse optimisation methodology, the reconstruction of the complex object wave $O(x,y)$ is formulated as an optimisation problem where we minimise a cost function given as

(3) $$ \begin{align} \begin{aligned} C(O,O^*) & = C_1 + C_2\\ & = \lvert\lvert H - (\lvert R \rvert^2 + \lvert O \rvert^2 + R^*O + RO^*) \rvert\rvert^{2}_{2} + \alpha \; \psi(O,O^*). \end{aligned} \end{align} $$

Here, the $\lvert \lvert ...\rvert \rvert _2^2$ represents the squared L2-norm of the quantity inside. The first term in the cost function represents the squared data fitting error between the measured hologram data $H(x,y)$ and the interference pattern formation model (equation (1)), whereas the second term $\psi (O,O^*)$ represents a suitable image domain constraint. The constant $\alpha $ denotes a positive regularisation constant that determines the relative weight between the two terms of the cost function. In the present work, we used the total variation (TV) penalty function as a constraint for the optimisation problem. TV is a popular edge-preserving penalty function that has been widely used in the imaging literature, which is suitable for the present image plane holography data. The TV penalty is defined as

(4) $$ \begin{align} \psi(O,O^*) = \iint \lvert \nabla O(x,y) \rvert \ dx \ dy, \end{align} $$

where $\nabla $ represents the two-dimensional numerical gradient operation. Further, we utilise an adaptive alternating minimisation scheme inspired by Sidky and Pan (Reference Sidky and Pan2008) for the reconstruction of the complex-valued object field $O(x,y)$ that does not involve empirical selection of any specific regularisation parameter $\alpha $ . The adaptive alternating minimisation scheme is already described in prior publications (Mangal et al., Reference Mangal, Monga, Mathur, Dinda, Joseph, Ahlawat and Khare2019; Singh & Khare, Reference Singh and Khare2017). The minimisation of cost $C(O, O^{\ast })$ is achieved iteratively. Since the unknown object function $O(x,y)$ is complex-valued, Wirtinger derivatives of $C_1$ and $C_2$ with respect to $O^*$ are evaluated to obtain the corresponding steepest descent directions. The Wirtinger derivatives of two terms $C_1$ and $C_2$ are given as

(5) $$ \begin{align} \nabla_{O^*} C_1 = -2\ \Big[ H - \lvert R + O \rvert^2 \Big]\ .\ (R + O) \end{align} $$

and

(6) $$ \begin{align} \nabla_{O^*} C_2 = -\ \nabla. \Big[ \frac{\nabla O}{\sqrt{\lvert \nabla O \rvert^2 + \epsilon^2}} \Big]. \end{align} $$

Here, $\epsilon ^2$ is a small positive number ( $\approx 10^{-10}$ ) used to prevent zero division. The essence of the optimisation process is that in each iteration, the numerical values of $C_1$ and $C_2$ are reduced in an adaptive manner, such that the change in the solution due to the reduction in $C_1$ and $C_2$ is balanced. The iterative process is stopped when the solution $O(x,y)$ changes negligibly in successive iterations. Since this optimisation process operates completely in the image domain, a region of interest can be suitably chosen to allow a full-resolution recovery of $O(x,y)$ over a region of interest of the recorded image plane hologram $H(x,y)$ . In other words, a user can easily select a region of interest near a pollen grain for the phase map recovery. In the present study, a $512 \times 512$ pixel area is used for phase reconstruction of individual pollen. Using the optimisation procedure, the complex-valued image field $O(x,y)$ is recovered with diffraction-limited resolution. The phase map $\phi (x,y)$ associated with this image field is defined as the ratio of imaginary and real parts of $O(x,y)$ :

(7) $$ \begin{align} \phi(x,y) = \arctan \Bigg( \frac{Im\ [O(x.y)]}{Re\ [O(x,y)]} \Bigg). \end{align} $$

Since the arc-tangent function is defined only for the range $[-\pi ,\pi ]$ , the phase map $\phi (x,y)$ retrieved from the optimisation procedure is in a wrapped form. In order to unwrap this phase map and derive the full physical information, a 2D unwrapping algorithm has been used that is based on the transport of intensity equation method (Pandey et al., Reference Pandey, Ghosh and Khare2016). The unwrapped phase function can be associated with the projection definition in equation (2).

3.1. Sample collection and pollen analysis

3.1.1. Sample collection and staining

Lantana camara flowers (see Figure 2a) were collected from Hauz Khaz Rose Garden (28 $^{\circ }$ 32’52.09”N/ 77 $^{\circ }$ 11’27.77”E), which is a part of Delhi Ridge forest. Fresh flowers were plucked early morning, which were then directly transferred to the laboratory for analysis. Pollen grains were extracted from florets and transferred on slide using the tapping and squashing method. For stain preparation, 2 g of Carmine powder was dissolved in 95 ml of glacial acetic followed by an addition of distilled water to make a 100-ml solution. The solution was boiled, filtered and stored at room temperature. Flower clusters (inflorescences) were collected when the clusters each had at least one flower partially open. Pre-dehiscent anthers were removed from unopened flowers and placed in a 1.5-ml Eppendorf tube with $\approx $ 100 $\mu $ L of acetocarmine stain. Anthers were stained and rinsed three times with distilled water. Care was taken not to burst the anthers while rinsing them. Rinsed anthers were squashed in 50 $\mu $ L of glycerol (diluted with 20% water) and transferred onto a microscope slide and covered with a cover slip. The slide was gently tapped and pressed to release pollen grains out of anthers. Pollen viability was then observed immediately through microscopic imaging.

Figure 2. (a) Lantana camara flowers, and typical Lantana pollen grain images observed with (b) an optical microscope and (c) a 20-kV scanning electron microscope. Note the surface texture and tricolpate nature of the pollen grain.

3.2. Species validation via scanning electron microscopy

The surface texture of pollen grains was examined using a SEM (EVOLS10, Carl Zeiss) and this was used to validate species identity. Specimens of selected viable Lantana camara pollen grains were prepared for SEM by fixing the pollen in 2.5 $\%$ (v/v) glutaraldehyde in a 0.1-M sodium phosphate buffer, vacuuming them thrice, then leaving them to dry for 24 hr. Samples were then coated with gold palladium using Sputter Coater SC7620, before observing under SEM. Images were captured using SmartSEM software and the images of the mounted pollen specimens were taken at bar 10 $\mu $ m. All procedures were performed as per the protocol of the manufacturer. The pollen unit was found to be monads or tetrads, with psilate-type sculpture and colpi largely tricolpate, as shown in Figure 2c. Quantitative parameters such as polar diameter, mesocolpium distance, equatorial dimensions, aperture size, spine diameter and exine thickness can be calculated from these images using the open-source ImageJ software (https://imagej.nih.gov/ij/).

3.3. DHM imaging of Lantana pollen

The DHM system used in our study (Make: Holmarc Opto-Mechatronics, Kochi, India, Model: HO-DHM-UT01-FA) works in dual mode, that is, both bright-field and holographic, as depicted in Figure 1. It employs a Nikon Fluor 40X, 0.75NA objective lens for imaging. The system uses an array sensor (Make: IDS GmbH, model: $\mu $ Eye CP-3070) with $3.4$ - $\mu $ m square pixels. The user can switch between the laser and LED illuminations for recording an image plane hologram or a bright-field imaging of the sample without physically disturbing it. Since the phase imaging is not a familiar modality among plant science researchers, the bright-field mode can help locate the individual pollen over the sample slide, which may be focused appropriately. The holographic mode which essentially involves switching of the illumination can then record an image plane hologram of a pollen in the same focused position. Numerical reconstruction as described in Section 2.3 applied to a recorded hologram then provides the user with the quantitative phase information $\phi (x,y)$ associated with each pollen grain. Since the phase map represents optical path length, it is a common practice to render it as a surface plot to provide a sense of depth information regarding the object being imaged. The speciality of our DHM system is that it provides single-shot phase imaging at the full diffraction limited resolution.