Spatial frequency modulated imaging (SPIFI) is an imaging method that utilizes a single-element detector to reconstruct an image by selectively modulating the input laser field. In this manner, extended excitation sources can be used for optimal image acquisition in scattering specimens. To date, SPIFI has been used in multiple modalities including second harmonic generation (SHG), third harmonic generation (THG), fluorescence imaging [1–3], hyperspectral imaging [4,5], fluorescent holographic imaging [6,7], and tomographic imaging [8–10].

Using this technique, the image is constructed by projecting a time-varying set of spatial frequencies onto a sample by modulating the illumination beam with a specifically designed mask [11]. The modulated beam is projected onto the desired sample, and the resultant light is collected on a single-element detector such as a photodiode or photomultiplier tube as a function of time. Once the complete set of modulated frequencies have been collected over the course of a single scan of the mask, a Fourier transform of the time signal is performed which results in a one-dimensional image of the sample. The image is centered on a carrier frequency set by the rotation rate of the mask, density of the mask features, and the radius of the beam center. 2D images can be made by scanning the beam or sample in the direction perpendicular to the line focus and repeating the data collection process. In addition to the fundamental image made from the reconstructed temporal signal, SPIFI also enables enhanced resolution imaging in all modalities, both linear and nonlinear [12]. This translates, in terms of the utility of the microscope, into the ability to exhibit the resolution of a higher numerical aperture (NA) over the field of view dictated by the intrinsic optical characteristics of the microscope.

The inherent advantages of the microscope system demonstrated here for the first time, include interferometric imaging with a long working distance (WD) optic (63 mm), submicrometer axial resolution, 10 μm lateral resolution, and a 20 mm field-of-view (FOV), all achieved with point detection located in the epidirection making the system compatible for use with turbid and scattering specimens. The WD and FOV make the system attractive for use in a diverse range of applications. Indeed, we have previously demonstrated real-time SPIFI amplitude modulation imaging commensurate with a femtosecond laser micromachining platform [13] when scattering layers are between the imaging optics and the sample. The addition of the new interferometric contrast modality detailed in this work enables real-time topological characterization in these applications [14]. Extracting information from interferometric images is an entire industry within itself; the intent here is to show for the first time, the facile creation of these images using I-SPIFI with multiple advantages following. Specifically, the I-SPIFI opens new design degrees of freedom for full-field interferometric microscopy: (1) single-element detection enables imaging through turbid/scattering media, (2) no specialized objectives (e.g., Mirau objective) are required, (3) the interferometer is a common path and simple to implement, (4) it can be seamlessly combined with nonlinear imaging modalities, (5) enhanced lateral resolution is enabled in all linear and nonlinear modalities, and (6) single-element detectors often offer superior performance compared to their two-dimensional counterparts.

In recent years, there have been many attempts at developing techniques that utilize single-element detectors to image and also record the phase of objects. Digital micromirror devices (DMD) [15,16], spatial light modulators (SLM) [17,18], and projectors [19] have been used as means to illuminate the sample with a desired set of patterns which are recorded and used to reconstruct the final image. These efforts have also been successful in using compressive sensing to record fluorescent and hyperspectral data and image through scattering media. The work presented in this Letter is intended as a complementary technology to the field of single-element detection imaging.

The modulation mask used in this SPIFI microscope was custom fabricated in-house by ablating a fused silica substrate with an amplified femtosecond laser [20]. The mask substrate is a 75 mm diameter, 3 mm thick disk that was ablated with the modulation pattern feature size down to 7 μm. The laser source for the microscope is a home-built all normal dispersion (ANDI) fiber laser with a central wavelength of 1040 nm [21]. The laser is operated in the continuous-wave (CW) regime for all the image series presented here.

The SPIFI microscope (Fig. 1) consists of a polarizing beam splitter (PBS) (Thorlabs PBS253) which transmits the input beam from the fiber laser. It is then focused by a cylindrical lens (Thorlabs LJ1567L2-B) so that the resulting light sheet is incident on the surface of the SPIFI modulation mask (MM). An average power of $\sim 9\mathrm{mW}$ was measured after the SPIFI mask and was used to illuminate the samples. The diffracted beams are image-relayed in a 4-f configuration to the sample plane by the relay lens (RL) (Thorlabs AC508-100-B-ML) and the final objective lens (OBJ) (Thorlabs AC508-075-B-ML). Before the objective lens, the beam propagates through a quarter-wave plate (QWP) (Thorlabs WPQ10M-1030). When the microscope is set up to collect in reflection, all of the reflected light from the sample passes back through the quarter-wave plate so that the signal light is reflected off the polarizing beam splitter at the entrance to the microscope. A lens (${\mathrm{L}}_{\mathrm{R}}$) (Thorlabs AC254-060-B-ML) then focuses the signal light onto a photodiode. In the transmission orientation, the light transmitted through the transparent sample is collected onto a photodiode by a lens (${\mathrm{L}}_{\mathrm{T}}$) (Thorlabs AC508-100-B-ML). In the transmission direction, the photodiode is placed at the location where the beam waists in both the focusing and nonfocusing directions are equivalent. This is the traditional detection plane for most SPIFI systems, and where theory and past experiments show, the image contrast is proportional to the spatially integrated intensity [3].

 

Fig. 1. Diagram of the SPIFI microscope with the integrated ${\mathrm{CO}}_2$ laser heating system. The enclosed dotted area highlights the common path interferometer portion of the microscope which makes spatial interferometric contrast imaging possible.

Download Full Size | PDF

In addition to the SPIFI microscope, a ${\mathrm{CO}}_2$ laser $(\lambda =10.6\mathrm{\mu m})$ is integrated into the system and directed by a mirror through a 25.4 mm diameter, 50 mm focal length ZnSe lens (${\mathrm{L}}_{{\mathrm{CO}}_2}$) which is placed such that the focal plane is incident on the sample. The focal spot can be moved relative to the location of the line focus produced by the SPIFI system. The ${\mathrm{CO}}_2$ system is electronically controlled to provide a momentary firing capability with pulses at a certain duty cycle and a repetition rate set by the user. An average power of 2 W was used with a firing time of $<0.25\mathrm{s}$.

In a SPIFI microscope, a common path interferometer is inherently built into the system. This interferometer can be seen in the enclosed dotted area of Fig. 1. Here, we exploit this geometry for the first time to create images sensitive to either path length differences within a sample (e.g., due to changes of the index of refraction) or a variation of the surface profile of the sample.

The common path interferometer is a result of the SPIFI modulation mask. A single-light sheet incident on the mask is diffracted after transmission through the mask, and the resultant orders interfere when imaged to the focal plane of the microscope. This interference results in the projection of a time-varying set of spatial frequencies onto the sample. In this system, we detect the excitation light in the epidirection back through the SPIFI mask. Consequently, all of the diffracted orders interfere once again on the return path back through the SPIFI mask. If no phase changes between any of the orders have occurred, the transmission is unperturbed. However, if any of the beams have been shifted in phase (either by a path length difference, or a change in direction), the interference pattern at the mask is disrupted. This disruption changes the net transmission through the mask, which is readily detected in terms of the measured amplitude of the signal at that spatial frequency.

Following the analysis of Field et al. [12], three beams are considered in the interference model which comprise the 0 and $\pm 1$ diffracted orders generated by the modulation mask. These three diffracted beams are shown in Fig. 1. The 0-order diffracted beam remains on axis, while the $\pm 1$ orders have an incident angle of $\pm \theta$ which varies as the mask is rotated over a complete scan. In a three-beam interferometer model, the signal contains three interference terms corresponding to the phase differences between the respective orders. An example of the modeled and experimental interference of the three diffracted orders for the return path at the plane just in front of the modulation mask is shown in Figs. 2(a) and 2(b).

 

Fig. 2. Signal interference of small displacements at the focal plane of the I-SPIFI system. (a) and (b) show the modeled and measured interference, respectively, with blue representing the unperturbed surface, and red the perturbed surface. (c) images of a 1951 AF resolution target collected in the transmission and reflection directions, highlighting the carrier frequency of the modulation remains the same in both modalities. The red line indicates the position of the I-SPIFI images. (d) The reconstructed image as a result of a linear increase in the displacement of the focal plane. This simple model tracks the dynamic experimental results in Fig. 3.

Download Full Size | PDF

Notably, for the distances (between the SPIFI mask and the specimen) and the mask rotation rates used here, the round-trip time through the common path interferometer is sufficiently short ($\sim 2\mathrm{ns}$) that the carrier frequency of the image is identical to that obtained when the mask is single passed. This has been verified experimentally, as the images captured in the transmission direction compared to the images captured by double passing the mask are centralized on the identical carrier frequency [Fig. 2(c)].

To create a pure phase object and examine a dynamic process, uncoated, 10 mm thick BK7 glass windows were heated with pulses from the ${\mathrm{CO}}_2$ laser. The ${\mathrm{CO}}_2$ light is absorbed by the material and results in thermal expansion of the surface which adds a path length variation along the imaging beam that encodes a specific amount of phase difference for each point along the line focus of the microscope. The BK7 glass sample was placed at the focal plane of the I-SPIFI microscope, and the ${\mathrm{CO}}_2$ laser was made incident at an angle on the same surface being imaged. The design allows for the ${\mathrm{CO}}_2$ laser spot to be placed in any location on or around the imaging light sheet. In the set of images displayed in Fig. 3, the I-SPIFI beam is held stationary, and 1D images were collected dynamically at a rate of 0.023 s per line image (43.5 Hz) before, during, and after firing the ${\mathrm{CO}}_2$ laser.

 

Fig. 3. Images of dynamic surface expansion of BK7 glass. (a) is the image in the reflection geometry, while (b) is in the transmission direction. The red dashed lines are indicative of when the ${\mathrm{CO}}_2$ laser was fired.

Download Full Size | PDF

By calculating the surface expansion properties of the BK7 glass, it is possible to see that a maximum value for the surface expansion of BK7 before it reaches its melting temperature of 830.2 K from room temperature ($\sim 298.2\mathrm{K}$) is $\sim 11.3\mathrm{\mu m}$, and at a temperature change of 100 K it is expected that the sample surface will expand by only $\sim 2.1\mathrm{\mu m}$. An Adafruit AMG8833 thermal sensor was used to qualitatively verify the surface temperature rise and thermal relaxation timescales. The ${\mathrm{CO}}_2$ laser was fired in short bursts at low average power (2 W) so that no melting or heat induced fracturing of the BK7 surface occurred, and the sample was observed to relax back to its equilibrium state after each set of images. The horizontal axis represents the spatial position along the imaging line focus, and the vertical dimension is representative of time, with the beginning of the scan at the top of the frames. Dashed horizontal red lines indicate the temporal location of the ${\mathrm{CO}}_2$ laser firing. In both parts of Fig. 3, the ${\mathrm{CO}}_2$ laser spot is placed on the left side of the imaging beam. This contributes to the wave-like structures being nonsymmetric along the image in Fig. 3(a).

Part (a) of Fig. 3 is an image in the reflection geometry, and (b) is the image in the transmission geometry. The lack of any change in the reconstructed image in transmission while the ${\mathrm{CO}}_2$ laser is fired is indicative of the image formation process discussed in the introductory section, as the signal laser light is spatially integrated on detection. Each high intensity point in Fig. 3(a) is indicative of a wavelength change in the surface expansion. Figures 2 and 4 quantify the image formation process in Fig. 3 experimentally and computationally. In Fig. 2, measured and computed spatial frequencies at the plane in front of the SPIFI mask are shown for the return path, while in Fig. 4, the measured and computed diffracted light sheets at the exit pupil of OBJ (Fig. 1) are shown.

 

Fig. 4. Modeled and experimentally measured 2D Fourier transforms of the three light sheets ($+1$, 0, $-1$ orders) of the I-SPIFI system at the exit pupil of OBJ (Fig. 1). (a) and (b) are the modeled 2D Fourier transforms of the unperturbed surface and the expanded surface, respectively, and (c) and (d) are the experimental images of the same surfaces.

Download Full Size | PDF

Images were made over a large field of view of transparent nail polish structures painted onto a glass microscope slide. To compare the new imaging method in this paper to conventional microscopy, a white light image was taken with a $100\times$ magnification microscope objective. The resulting white light image is seen in Fig. 5(a). This figure is a composite of 70 individual 2D images and shows almost no contrast over the extent of the specimen. Figure 5(b) is the I-SPIFI image. The I-SPIFI image shows marked contrast and brings out features that are not apparent/recognizable in Fig. 5(a).

 

Fig. 5. Comparison of white light and I-SPIFI images of transparent polish on a glass substrate. (a) 70 frame composite white light image using a $100\times$ objective. (b) I-SPIFI image of the same transparent polish structure.

Download Full Size | PDF

To highlight the axial sensitivity, it is only necessary to digitally zoom in on topological features where fringing is evident (Fig. 6). The figure shown here is an example of how I-SPIFI can be used to perform full-field interference microscopy (for examples of full-field interference images see the review by deGroot [14], Fig. 14) In this form of microscopy, quantitive topology at subwavelength resolution is established by tracking the peaks of the fringing formed in the images. One of the key advantages of I-SPIFI is notable in Fig. 6(b), the enhanced resolution (second order) image. As evident in the image, the enhanced resolution afforded by I-SPIFI enables higher fringe contrast, as the lateral resolving power of the optical system is increased by a factor of two in this case [11].

 

Fig. 6. I-SPIFI images of polish on a microscope slide. Fringing reveals the topology of the structure and is evident in (a) the fundamental resolution image, and is seen even more clearly in (b) the second order image.

Download Full Size | PDF

Finally, two microscope slides were pressed together, and images of the Newton rings formed at the interface were recorded. As in Figs. 3 and 6, the fringes in these images indicate that the I-SPIFI microscope is sensitive to the path length traveled by the laser light in submicron increments as the peaks of the fringes can be clearly resolved.

The sample was rotated by 90 deg between Figs. 7(a) and 7(b). This helps illustrate that the interference fringes track appropriately with the specimen characteristics, and are not a result of an effect caused by the scan direction or the orientation of the line focus.

 

Fig. 7. I-SPIFI images of Newton rings between two microscope slides. (a) and (b) are images of a Newton ring sample that were formed at orthogonal orientations to show that the fringes track with the orientation of the sample.

Download Full Size | PDF

In this work, we have demonstrated I-SPIFI for the first time. We have modeled and measured the system performance with a series of specimens that demonstrate the interferometric capability: the reversible expansion of a glass surface when heated (Fig. 3), the difference in material properties not readily visible with traditional white light microscopy (Fig. 5), full-field interference imaging (Fig. 6) with and without enhanced resolution, and interference patterns from interfaces (Fig. 7). We have modeled the system using three-beam plane wave interference [12], and benchmarked calculations by measuring the resulting signals as they are reflected back through the system (Figs. 2 and 4).