1. Introduction

Endoscopes for different imaging modalities experience a rapid evolution in modern medical and biomedical applications. In-vivo observations of biological tissue at hardly accessible regions require miniature optical systems to project the observed volume outside of the specimen while magnifying it simultaneously and therewith decreasing the image-sided numerical aperture (NA) for an easier scanning and hence easier digitalization. Particularly promising are confocal or quasi-confocal processes which allow for optical sectioning. Yet, successful microscopic imaging of in-vivo tissue with a micron scale resolution requires an adaptation of the needle-like endoscope to the targeted imaging modality. In practice, research approaches of endomicroscopic applications reach from single photon processes like optical coherent tomography [1–4] and confocal single photon fluorescence processes [5–9] to multi-photon-imaging modalities like second-harmonic-generation [10, 11], multi-photon-fluorescence [12–18] and coherent-anti-raman-spectroscopy [19, 20]. In either case, a minimal volume expansion of the probe, high object-sided NA, large field of view (FOV), diffraction-limited spot-to-spot quality and in some of the latter mentioned cases also a good chromatic correction are quality criteria of the probes.

Within this work, we focus on the optical and mechanical design as well as experimental evaluation of high-resolution microobjectives working confocally in epi-fluorescence mode. Previously performed experiments showed a significant increase of the usable field of view in comparison with a state-of-the-art system and hence motivated for further research [21]. The optical performance requirements are very strict including a low spherical aberration and a precise color correction within the specified wavelength range while maintaining the high resolution for the entire FOV.

Especially useful for endomicroscopic imaging systems are simple GRIN-lenses or GRIN-based assemblies due to their plane geometrical surfaces as well as their potentials for aberration correction. The radial refractive profile of focusing lenses usually consists of a nearly parabolic shape of the refractive index profile which decreases progressively towards the edge of the rod lens. Yet, the refractive index profile can be aspherically adapted to overcompensate the monochromatic aberrations induced by the preceding standard optical components leading to an overall quality improvement. In such a case, the profile can be described by a Taylor expansion, n_r = n₀ + n₂ · r² + n₄ · r⁴ + ..., with n_r being the refractive index at the distance r from the optical axis, n₀ being the refractive index at the center and n₂ and n₄ being the second and fourth order polynomial coefficient, respectively. The odd orders disappear because of the axial symmetry by definition. Production-related limitations in the refractive index difference between the center and the margin of the lens of less than 0.14 result in a limited object-sided NA of about 0.5 and hence make it obligatory to use additional micro-components to achieve the targeted value of 0.8. A high NA is important since its magnitude scales by Abbe’s-theory inversely with the minimal resolvable lateral structure size ${\mathrm{\Delta }}_{\text{Lateral}}=p_L\frac{\lambda }{\text{NA}}$ and inversely squared to the minimal axial resolution ${\mathrm{\Delta }}_{\text{Axial}}=p_A\frac{n\cdot \lambda }{{\text{NA}}^2}$. Those values coincide with the radii of the lateral and axial FWHM of the ideal PSF’s whose prefactors are p_L = 0.51 and p_A = 1.76. For the confocal case, those constants progressively decrease down to p_L = 0.37 and p_A = 1.28 for an infinitesimal small pinhole and a neglected wavelength shift for fluorescence experiments [22].

2. Design methods

2.1. Optical design concepts of the endoscopic systems

A starting point for the upcoming designs was an internally available product at GRINTECH (NA_ob: 0.8; color correction: 488 nm – 550 nm; diameter including mounting: 1.4 mm; Magnification: 2.5 to 3; Mechanical length: about 5 mm). An evaluation of this precursor system for comparison reasons is part of the study. Preceding investigations showed a good on-axis performance for this device but a reduced imaging quality for progressively increasing off-axis field points and hence motivated for further research. Results have been published for a similar catalog system GT-MO-080-0415-810 [14–16] which in contrast targets multi-photon imaging processes and therewith operates without the need of color correction elements.

A sketch of the precursor design is depicted in Fig. 1 (left). The probe consists of a window mounted on a plano-convex lens (radius of curvature: 0.5 mm; center thickness: 370 μm), entailed by two different GRIN-lenses (specifications from left to right: 1.0 pitch length: 9.6 mm/13.92 mm @λ =488 nm; length: 1.31 mm/3.0 mm) and a diffractive optical element (DOE) specifically designed for the color correction from 488 nm to 550 nm (focal length @λ =488nm: 5 mm and @λ =550 nm: 4.43 mm). A pure second order phase term describes the progressively decreasing distances between consecutive structures of the DOE with a minimal structure between consecutive rings of 4.8 μm. The GRIN-lenses have slightly aspherical refractive index profiles resulting in a not negligible but relatively small n₄ coefficient leading to a correction of spherical aberrations and thus increase of the optical spot-to-spot quality. The setup is optimized for a working distance of 60 μm in water with the formation of its diffraction-limited image at the back surface, making the assembly especially useful for high-NA multicore imaging fiber bundle applications. Yet, the design is purely on-axis corrected which results in a resolution decrease of outer zones. Field points more than 20 μm apart from the optical axis experience aberrations and thus do not ensure a diffraction-limited NA of 0.8. Figure 1 (right) depicts the image sided polychromatic modulation transfer function (MTF) - evaluated at 488 nm and 550 nm - depending on the object field zone for frequencies of 100, 400 and 800 cycles per millimeter, which illustrates this tendency.

 

Fig. 1 Precursor system: Consists of a BK7-window, a high-refractive index plano-convex lens and a DOE sandwiched between two GRIN-lenses with different, special adapted GRIN-profiles; NA_Object=0.8; NA_Image=0.326; Lateral magnification: −2.61; Color corrected for 488 nm – 550 nm to match beam paths of excitation and emission wavelengths for confocal, single photon fluorescence measurements; Drawback: progressively decreasing performance for off-axis zones as indicated by the polychromatic MTF vs. field for 488 nm and 550 nm (right).

Download Full Size | PDF

A variety of producible designs with an object-sided NA in the range from 0.5 to 1.0 and a corresponding diffraction-limited FOV reaching from 600 μm to 180 μm in diameter respectively evolved at a foregoing design study whereas the two most promising results implying the cost-benefit ratio have been selected for the production and are presented in the following. Similar to the precursor, the mechanical constrains of 1.4 mm in diameter and about 5 mm length are retained whereas the intrinsic complexity of the optical components is increased. Furthermore, an object sided telecentricity is assumed. Some distortion and field curvature have been accepted leading to a well feasible complexity while enabling a small spatial extend of the probe. This compromise is justified as the main application is in biological and biomedical areas and the observation of only two dimensional specimens in these fields rather limited. The influence of distortion and field curvature can be numerically subtracted from the z-stack measurement if the amount of those aberrations is precisely determined beforehand. Planapochromates prevent the necessity of the numerical readjustment by including meniscus lenses at either the distal or proximal side of the endoscopic system [23–25]. However, the incorporation would essentially complicate the assembly, enlarge the probe and in addition make the handling for the end-user more difficult. Therefore, it is refrained from implementing meniscus lenses. Yet, the toleration of field curvature doesn’t imply a minor importance of axial aberrations. Their magnitude strongly influences the sensitivity and hence the signal to noise ratio of confocal measurements.

A first design focuses on the correction of chromatic aberrations by the incorporation of a DOE and hence the use of diffractive effects (design DiPolyC). The system - sketched in Fig. 2 (left) - consists of a sapphire window for a good scratch and crack resistance entailed by two plano-convex lenses (specifications from left to right: radius of curvature: 0.7 mm/1.85 mm; center thickness: 0.74 mm/0.53 mm), a DOE for the color correction (focal length @λ =488nm: 6.68 mm and @λ =550 nm: 5.92 mm) and finishes up with a GRIN-lens (1.0 pitch length: 16.46 mm @λ =488 nm; length: 3.39 mm).

 

Fig. 2 Design DiPolyC: Consists of a sapphire window, two high refractive index planoconvex lenses, a DOE and a GRIN-lens with a highly aspherical profile; NA_Object=0.8; NA_Image=0.308; Lateral magnification: −2.58; Color correction 488 nm – 550 nm; Advantage: significantly stabilized off-axis imaging quality as indicated by the polychromatic MTF vs. field for 488 nm and 550 nm (right).

Download Full Size | PDF

In contrast to the precursor, the radial phase function of the DOE is a sixth-order polynomial with a minimal distance between consecutive structures of 6.8 μm. Additionally, the GRIN-lens has a strongly aspherical profile, meaning a much higher n₄ coefficient in comparison with the corresponding lens of the precursor leading to additional degrees of freedom and thus to an enhanced quality improvement ability. The object sided working distance in water is fixed to 80 μm whereas the image sided working distance set to 100 μm in air simultaneously. Figure 2 (right) depicts the corresponding polychromatic MTF depending on the object field zone, which predicts a diffraction limited performance, resulting in a Strehl ratio of more than 0.8 for objects up to 300 μm in diameter. The tendency of a slight resolution decrease of the tangential plane towards increasing object zones induced by the incipient vignetting effect is well illustrated. While DOE’s possess a strong potential of color correction, their performance is constricted due to a limited diffraction efficiency in the design order over larger wavelength ranges as well as imperfect pattern structures. For confocal fluorescence measurements, these effects will lead to an intensity drop and in general involve the risk of ghost images. Zemax doesn’t allow for a realistic evaluation of the DOE which thus is to be assumed to diffract the light solely in the design order. However, especially the effect induced by neighboring diffraction orders is not negligible in the case of a not perfectly produced DOE and their influence is thus analyzed in the following paragraph.

The diffraction efficiency and hence the influence on the imaging performance of the undesired orders of the DOE for a blazed grating is significantly reduced [26]. A simplification of the simulation becomes feasible in which just the direct neighboring orders - hence the zeroth and second order - are considered to influence the performance. Thus, the influence of the higher and lower orders is neglected in the subsequent evaluation. The simulation - realized with Zemax and MatLab - assumes an on-axis point source in the image plane emitting at 488 nm and a complete frequency conversion of energy to a wavelength λ of 550 nm in the focus position at the specimen. Hence, the PSF at the object for 488 nm is convolved with the PSF at the image for 550 nm and the amount of energy determined which passes a pinhole at the location of the perfect light source in the image with the size of one airy diameter (2.2 μm; @λ =550 nm). To simplify the simulation two slightly different cases are considered. Firstly, it is assumed that the DOE works perfectly for either the zeroth, first or second diffraction order for the illumination and detection (Fig. 3(a)). Strong axial chromatic and increased spherical aberrations lead to a decreased energy narrowing at the pinhole position for the frequency converted light. The ratio between the energy which passes the pinhole (E_Detected) and the energy which is emitted at the point source in the image plane (E_Emitted) is calculated and is consequently a measure for the influence of the considered diffraction order.

 

Fig. 3 Evaluation of the influence of the undesired diffraction orders of the DOE on the imaging performance for confocal single photon fluorescence imaging processes; The calculation is performed by convolving the PSF in the object plane (λ =488 nm) with the PSF in the image plane (λ =550 nm) while assuming a complete conversion of the energy at the specimen; The table on the left presents the ratio between the detected (E_Detected) and emitted amount of energy (E_Emitted) passing through the on-axis pinhole in the image plane of the size of one airy diameter (2.2 μm; @λ =550 nm); the DOE is assumed to work perfectly in either the zeroth, first or second diffraction order for the illumination and detection for case (a); the DOE is assumed to work perfectly in the first order for the illumination and perfectly in either the zeroth, first or second diffraction order for the detection in case (b) (η_0/1/2 is the diffraction efficiency of the corresponding order).

Download Full Size | PDF

Less than 0.4 % of the emitted energy passes the pinhole if the light is diffracted in the zeroth or second diffraction order, respectively. In contrary, 75% of the emitted energy passes the pinhole if the light is diffracted in the first order. Realistically, those values have to be multiplied with the square of the efficiency η_0/1/2 of the corresponding order which further decreases the influence. Secondly, the zeroth and second order are neglected for the illumination. Thus, the light from the specimen (550 nm) propagates towards the intermediate image solely from the spot of the focus in the ideal working distance. This light diffracts in different orders during the propagation towards the image plane as sketched in Fig. 3(b). The fraction of the light passing the pinhole is evaluated and shows that just 0.005% of the emitted light multiplied with the corresponding efficiencies pass the pinhole.

Summarized, this first order approximation shows that ghost images induced by undesired diffraction orders are almost perfectly prevented for confocal fluorescence imaging modalities even if their diffraction efficiencies are not negligible. Contrarily, a decrease of the measuring speed in quadratic dependence of the diffraction efficiency of the design order will occur.

A second auspicious design approach overcomes the occurring chromatic spatial separation of the foci by the use of an achromatic spherical lens doublet and hence by refractive optics (design RePolyC). Figure 4 depicts a sketch of the setup consisting of a sapphire window, entailed by two plano-convex lenses, an achromatic lens doublet (specifications from left to right: radius of curvature: 0.6 mm/1.05 mm/2.6 mm; center thickness: 0.63 mm/0.48 mm/1.0 mm) and finishing up with an adapted GRIN-lens (1.0 pitch length: 16.46 mm @λ =488 nm; length: 3.09 mm). Incipient vignetting effects slightly decrease the resolution especially in the tangential direction of progressively increasing off-axis zones leading to a Strehl ratio which falls below a value of 0.8 for object zones with a diameter of more than 250 μm. Yet, this design shows a great potential since it relies entirely on refractive effects and omits the use of a DOE.

 

Fig. 4 Design RePolyC: Consists of a sapphire window, two high refractive index planoconvex lenses, an achromat and a GRIN-lens with a highly aspherical profile; NA_Object=0.8; NA_Image=0.277; Lateral magnification: −2.87; Color correction 488 nm – 550 nm; Advantages: the omission of a DOE and significantly stabilized off-axis imaging quality as indicated by the polychromatic MTF vs. field for 488 nm and 550 nm (right).

Download Full Size | PDF

Furthermore, Fig. 5(a) depicts the Strehl ratio for an on-axis field point and Fig. 5(b) for a 100 μm (object-sided) off-axis field point for RePolyC (right), DiPolyC (middle) and their precursor (left) as a function of the object-sided working distance and the wavelength. The black lines confine the region in the density plot with a Strehl ratio larger than 0.8 and hence emphasize the region with a diffraction limited point-to-point imaging quality. The graphic demonstrates a low on-axis spherochromatism for the extended spectrum for all three systems but a limited on-axis achromatism for the precursor and DiPolyC when moving away from the design wavelengths. Contrarily, RePolyC shows a limited on-axis and off-axis axial chromatic aberration even for the extended spectral range. Moreover, the influence of field curvature is shown for DiPolyC and RePolyC by comparing the on-axis and off-axis focal positions for a chosen wavelength.

 

Fig. 5 Monochromatic Strehl ratio of the on-axis (a) and 100 μm (object-sided) off-axis (b) field point as a function of the object-sided working distance and the wavelength evaluated for the precursor (left), DiPolyC (middle) and RePolyC (right), respectively; the black lines confine the region with a Strehl ratio larger than 0.8 and thus predict a diffraction limited imaging performance; the improved off-axis correction for the recent developments as well as a good spherochromatic and axial chromatic correction for the targeted wavelengths of 488 nm and 550 nm is obvious; RePolyC shows additionally a finite on-axis and off-axis axial chromatic aberration for the extended spectral range.

Download Full Size | PDF

2.2. Prototype fabrication

Tolerancing simulations with Zemax and MatLab indicated, that tight fabrication tolerances and an accurate alignment of the elements are strict requirements to achieve the desired performance. Figure 6 depicts a few components and sub-assembling groups of the produced probes. Small chips at the boundaries of the lenses occurred during the production process, especially for the very soft, high refractive index materials. Besides, measurements showed a high precision of the radii of curvature, the diameters and thicknesses of the elements.

 

Fig. 6 Single elements and sub-assembling groups of the endomicroscopic devices DiPolyC and RePolyC.

Download Full Size | PDF

The production of the GRIN-lens which has an identical profile for DiPolyC and RePolyC as well as the assembling procedure have been subsequently realized by GRINTECH. GRIN-TECH has been specializing for many years on the production of special GRIN-lenses with refractive index profiles deviating slightly from standard distributions as found in catalog elements. However, the fabrication of a stronger deviating profile as it is implemented in those objectives, meaning a n₄ coefficient much different from zero, demanded unprecedented procedures.

The fabrication of the GRIN-profile for conventional GRIN-lenses is described in the literature [26]. A variation of the silver and sodium concentration of the melts as well as the selected temperature and diffusion time strongly influence the final GRIN-profile. The determination of appropriate boundary parameters for the multiple ion exchange procedure based partly on state-of-the-art processes but yet required an iterative adaptation. Every rod lens was subjected to a wavefront measurement utilizing a Shearing interferometer to precisely evaluate the accordance of the GRIN-profile with the design. A match of the measured wavefront with the ideal wavefront shape was aimed and realized by a comparison of the Zernike fringe polynomials up to the 4^th radial order. Parts of the measured wavefront represented by Zernike fringe polynomials of 6^th and higher orders have been considered as uncontrollable aberrations and their magnitude reduced within the iterative procedure.

Figure 7 (left) depicts the experimentally measured wavefront of a quarter pitch GRIN-lens with the same GRIN-profile as incorporated in DiPolyC and RePolyC. The desired significantly strong fourth order spherical aberration induced by the adapted n₄ parameter is clearly seen. Subtracting the desired part reveals the unwanted residual fraction induced by the higher order polynomial coefficients of the GRIN-profile, n₆, n₈, n₁₀ and so on, which is depicted in Fig. 7 (right). Its RMS value could be decreased within the iterative production procedure to less than 0.126 wavelengths (@ 633 nm) which predicts an increase of the spot size by a factor of about 1.5 and hence a slight decrease of the performance of the probes. Currently ongoing process and simulation investigations aim for an even better adaptation of the experimental GRIN-profiles to the design requirement.

 

Fig. 7 Desired, experimentally determined wavefront at 633 nm of the GRIN-lens measured with a shearing interferometer (left); Remaining undesired higher order aberrations of the same wavefront after subtracting a Zernike fringe fit up to 4^th order; transverse axes normalized on unity and W scaled in wavelengths (@ 633 nm).

Download Full Size | PDF

3. Experimental evaluation

3.1. Field zone dependent resolution

Firstly, the devices have been subjected to simple imaging evaluations to determine the lateral magnifications by placing them in front of a camera (LuCam 135LW, Pixelsize 4.65 μm) with a microobjective (10x, NA 0.25) in such a manner that the produced image of the endoscopic systems coincide with the object plane of the mentioned MO. Subsequently, a lithographic test grid with 16 μm line period was placed in contact with the endoscopic system at the object side, illuminated with incoherent light at 488 nm in transmitted-light mode and moved apart till the working distance was met and thus a sharp image obtained. Therewith, magnification parameters for the presented designs could be confirmed for the precursor to be −2.65±0.05 (design: −2.61), for DiPolyC −2.55±0.05 (design: −2.58) and for RePolyC −2.93±0.13 (design: −2.87).

A more elaborated setup similar to end user applications was used - as shown in Fig. 8 - to qualify the field dependent axial and lateral resolution. A confocal laser scanning microscope ”Olympus Fluoview FV 1000” equipped with a semiconductor laser (Coherent, OBIS, 488 nm) was setup to scan the intermediate image of the endomicroscopic systems. To minimize intensity losses resulting from a NA mismatch, we chose a UPlanSApo 10x 0.4NA from Olympus with a 170 μm BK7 cover glass. Furthermore, a miniaturized x-y-z micrometer positioning stage with a 3D printed mounting was utilized for an accurate positioning of the micro-optics. While the optical design considered a biological tissue-like medium in object space with a refractive index close to water, an air gap was used instead since the beads and fluorescine layers of subsequent measurements were not stable in its position and the working distance was too tight for the use of a cover glass.

 

Fig. 8 Experimental setup for the evaluation of the endoscopic GRIN-objectives; the object imaged by the endoscopic system was scanned and digitalized confocally by the use of a laser scanning microscope; a self build x-y-z micrometer positing system enabled a precise positioning of the two objectives to each other.

Download Full Size | PDF

Figure 9(a) depicts images of subresolution fluorescence spheres (FluoSpheres Carboxylate 0.2 μm yellow-green 505/515, 2% solids) at selective lateral distances from the optical axis observed through the probes. Therefore, the solvent including the spheres has been diluted 1:10.000 in water and dried on a glass wafer to obtain a target with spatially isolated point sources. Subsequently, the specimen was irradiated at 488 nm and the signal measured confocally in fluorescence mode in the range from 505 nm to 540 nm. Precise values for the size of the airy diameter at the image pinhole plane are not extractable since this location is not accessible directly. However, its size was estimated to be roughly 90 μm in diameter and the pinhole narrowed down to 50 μm. The laser intensity as well as the voltage applied to the photo multiplier have been adapted for every image in this figure separately to obtain equally bright peak intensities. The applied power has been varied in a range of 3 μW to 25 μW measured at the intermediate image plane. A fast resolution decrease for image zones with a radius of more than 200 μm have been observed for the reference probe. Contrarily, the PSF’s produced with DiPolyC and RePolyC indicated a good imaging performance for radii of up to 400 μm.

 

Fig. 9 (a) Confocal images of subresolution beads (FluoSpheres Carboxylate 0.2 μm yellow-green 505/515, 2% solids, diluted 1:10.000 in water) observed through RePolyC (left), DiPolyC (middle) and their precursor device (right) for progressively increased image zones (top to bottom); Excitation at 488 nm and detection from 505 nm to 540 nm with an adapted laser intensity for every measurement; The increased performance for RePolyC and DiPolyC in comparison with the precursor is obvious; Scale bar corresponds to 2 μm in image plane (b) confocal z-stack of a subresolution sphere in fluorescence mode with DiPolyC at a lateral distance of 50 μm from the optical axis in the image plane; Scale bar corresponds to 2 μm in image plane (c) Determination of the corresponding axial FWHM in the object plane by a Gaussian fit to the intensity maximums I_Max(z) of the lateral Gaussian fits.

Download Full Size | PDF

Subsequently, the axial PSF was extracted by measuring the intensity distribution in multiple axial positions close to the circle of least confusion as depicted exemplary in Fig. 9(b). Every lateral measurement was fit by a MatLab routine with a two-dimensional Gaussian function to extract the sagittal and tangential FWHM respectively and to determine the peak intensity I_Max(z) of the Gaussian for every slice. Consecutively, the axial FWHM was determined by fitting a one-dimensional Gauss profile to the peak intensities I_Max(z) of the lateral fits as shown in Fig. 9(c).

Figure 10 depicts the lateral and axial FWHM of the PSF in the object plane depending on the distance from the optical axis. Therefore, the determined lateral FWHM-values in the image plane have been divided by the lateral magnification to obtain the lateral FWHM in the object plane. However, we achieved direct values for the axial FWHM at the object space since the probes have been connected physically to the MO and hence followed the movement for the z-stack measurements (see Figs. 10 and 11). Every measurement represents the averaged result of five separately performed experiments with identical microscope settings as described in the previous paragraph. The graph indicates that the axial as well as lateral on-axis resolution is comparable for all probes within the uncertainty of the measurement. However, it confirms the off-axis resolution to decrease quite rapidly for the precursor device while the two recent developments showed a good resolution within more than 200 % of the FOV radius of the precursor. This effect seems especially strong in the axial direction which leads to a significant decrease of the sensitivity for confocal measurements due to a smearing of the PSF. The indicated diffraction limit in the graph is calculated utilizing the prefactors for the conventional rather than for the confocal case.

 

Fig. 10 Experimentally measured lateral (left) and axial (right) resolution of RePolyC (green), DiPolyC (blue) as well as their precursor (red) depending on the radial size of the corresponding object zone; the later FWHM values are converted to the object plane by dividing by the lateral magnification; the axial FWHM’s are measured in the object plane directly since the MO is physically connected with the endomicroscopic objective.

Download Full Size | PDF

Figure 11 depicts the result of an axial image stack for DiPolyC and RePolyC at a lateral position of 369 μm from the optical axis in the image plane. For the precursor, significant off-axis aberrations decreased the imaging performance at the selected distance which prohibited a similar measurement due to occurring bleaching effects and a large signal to noise ratio. The graphs show the dependence of variation of the lateral FWHM with the axial distance z for the tangential (T) and sagittal (S) direction of the PSF (black lines). Besides, the figure depicts the normalized peak intensities of the corresponding lateral Gaussian fits (red lines). Three lateral measurements - confined by the blue bar - closest located to the axial intensity maximum have been averaged using the tangential and sagittal plane to obtain a quantitative measure for the lateral FWHM. The graphs indicate a decreased resolution for the tangential plane in comparison with the sagittal plane. This behavior was well repetitive between consecutive measurements and could be caused by the incipient vignetting effect (compare Figs. 2 and 4).

 

Fig. 11 Analysis of tangential (T) and sagittal (S) resolution (black lines) and the axial peak-intensities (red lines) for every slice of the z-stack by evaluating the PSF at an image height of 369 μm; the FWHM values are converted to the object plane by making use of the magnification; determination of the lateral FWHM’s at the circle of least confusion by averaging the values for the tangential and sagittal plane confined by the blue bar (compare Fig. 10).

Download Full Size | PDF

3.2. Sensitivity

In confocal and non-linear microscopy, a critical quality parameter of the optical setup is how much excitation laser energy needs to be applied to the sample, i.e. the tissue of interest, to record a low-noise image with significant information. Physically, this sensitivity parameter can be described by the ratio of how much fluorescence intensity passes the imaging pinhole per excitation laser intensity. Multiple effects contribute simultaneously to a reduction in sensitivity in the experiment, as for example monochromatic and polychromatic aberrations, internal scattering and reflections as well as diffraction losses. A separated consideration of the residual chromatic axial aberration could not be determined explicitly since the only available laser source in the specified wavelength range was emitting at 488 nm. At first, confocal fluorescence experiments aimed on the comparison of the fitted peak intensities of the fluorescence beads for different configurations but occurring bleaching effects led to non-reproducible variations and hence made the measurements not useful. A second approach focused on the scan of a thin homogeneously distributed fluorescence layer. Green Stanger text markers turned out to contain green fluorescent ingredients (fluorescine) with its absorption peak at 494 nm and emission maximum at 521 nm. One surface of a microscope slide was covered homogeneously with the fluorescent liquid of the text marker and the resulting layer rested until it was dried. A reflection measurement on a polished mirror surface with an UplanSApo 20x 0.75 NA objectiv averaged over five separately produced samples led to an axial resolution of the microscope of 1.36±0.06 μm. Subsequently, the fluorescine layer has been observed confocally in fluorescence mode for five samples leading to an axial FWHM of 2.22±0.09 μm. Under the assumptions that those two contributions are perfectly Gaussian, the wavelength shift at the fluorescence measurement is negligible and the microscopic objective perfectly corrected for chromatic aberrations in the specified wavelength range one can extract the axial thickness of the fluorescine layer by deconvolution to be 1.76±0.16 μm. The left three columns of Fig. 12 show the layer observed through the corresponding endomicroscopic systems at selective axial distances using an UplanSApo 10x 0.4 NA. The voltage applied to the PMT was locked to stay slightly below saturation for the on-axis position of the precursor, the cw-laser at 488 nm fixed at 3.5 μW output power measured at the intermediate image plane and the pinhole diameter adjusted at 50 μm in diameter. Concentric rings evolve around the center of the optical axis since the devices are not corrected for field curvature. In total, 50 images have been measured axially 250 nm apart from each other and their highest intensities projected on a plane surface to get a response for the entire FOV as seen on the right side of Fig. 12.

 

Fig. 12 Confocal images of a 1.76±0.16 μm thick fluorescine layer measured with DiPolyC(middle), RePolyC (botton) and their precursor (top) at selective axial distances of the image side (left) and the respective highest intensity projections (right side); the images are scaled in the image plane of the GRIN-systems whereas the red circles symbolize the margin of the back surface of the corresponding GRIN-system with a diameter of 1 mm; excitation light: 488 nm; MO: UplanSApo10x0.4 NA; white scale bar corresponds to 100 μm in object plane, respectively.

Download Full Size | PDF

The result shows how significantly better the sensitivity can be maintained over a much larger field of view for DiPolyC and RePolyC in comparison with their precursor, as predicted by the MTF’s presented in section 2.1. Furthermore, Fig. 13 (left) depicts the results for an absolute comparison and illustrates the intensity cross-section of the highest intensity projections. Similarly, the homogeneity for the recently developed devices is stated by the graph which shows an especially striking behavior for DiPolyC. Moreover, a high on-axis sensitivity is stated likewise for RePolyC and the precursor but a rather limited magnitude for DiPolyC. However, in contrast to the precursor, the prototypes of DiPolyC and RePolyC served as a proof of principle so far and thus omit anti-reflection coatings of the single components. An estimate for the amount of light which is lost hereby can be extracted from the refractive index coefficients of the corresponding surfaces by the Fresnel equations and the simplification of normal incidence $R={\left|\frac{n_1-n_2}{n_1+n_2}\right|}^2$. Since the light propagates in forward and backward direction through the probe, the amount of transmitted light at every interface has to be considered twice. The transmission for the round trip through the device led to a highest possible transmission factor of T_1,DiPolyC=44.9% and T_1,RePolyC=51.2%. A second influence is caused by the NA-mismatch at the intermediate image plane, leading to a loss proportional to the square of the ratio between the NA of the MO (NA_MO = 0.4) and the NA of the backfocal plane of the probe (NA_DiPolyC: 0.308; NA_RePolyC: 0.277; NA_Precursor: 0.326), ${\text{T}}_2={\left|\frac{{\text{NA}}_{\text{Probe}}}{{\text{NA}}_{\text{MO}}}\right|}^2$. Multiplying T₁ and T₂ for every system, respectively, leads to the factor which predicts the best possible output for a perfect matched image sided NA and the total reduction of all reflection losses within the device. As a result, the intensities of the left graph of Fig. 13 were divided by those factors, i.e. T_Precursor = 0.664, T_DiPolyC = 0.266 and T_RePolyC = 0.246. A subsequent normalization leads thus to the right side of the same figure.

 

Fig. 13 Experimentally measured confocal PSF intensity response averaged over four samples of a 1.76±0.16 μm thick fluorescine layer for RePolyC (green), DiPolyC (blue) and its precursor (red) (left); Predicted PSF intensity response when all surfaces would be anti reflection-coated and the NA of the MO would be matched with the NA of the GRIN-objective at the intermediate image plane (right); The radial distance is converted to the object plane by using the lateral magnification of the corresponding probe.

Download Full Size | PDF

Therewith, the highest on-axis sensitivity is stated for RePolyC, followed by an almost equal amount for DiPolyC and their precursor. In the case of negligible on-axis aberrations for all three systems, which seems a justified approximation when evaluating Fig. 10, the sensitivity difference for the on-axis points is mainly caused by the diffraction efficiency losses of the DOE due to fabrication imperfections. Hence, by comparison with RePolyC, the observed effect can be explained by a diffraction efficiency of 64±4% for the DOE incorporated in DiPolyC and 59±3% for the precursor. Moreover, the just mentioned diffraction efficiency difference is comprehensible by the minimal structure difference between consecutive rings of 6.8 μm for DiPolyC and 4.9 μm for the precursor. The smaller this value, the more deviations from the perfect structure are expected especially at the sharp edges resulting in a progressively decreasing agreement between a perfectly blazed structure and the real DOE and thus a decreasing diffraction efficiency.

4. Conclusion

Hereby, we described and demonstrated recently developed GRIN-based endomicroscopic objectives, DiPolyC and RePolyC, which considerably improved the imaging capability for confocal fluorescence imaging modalities in comparison with a precursor device. Previous evaluation experiments confirmed a good on-axis performance but a decreasing imaging quality towards the edge of the FOV for the state of the art system. Therefore, the recent developments aimed at an increased imaging performance for the outer zones of the field of view. For a better comparison and progress evaluation, we confronted the design concept of the two new developments with the state-of-the-art endomicroscopic objective. All discussed objectives possess similar extrinsic properties, i.e., a length of about 5 mm, an overall diameter of 1.4 mm, a color correction from 488 nm to 550 nm, an object sided numerical aperture of 0.8 and an image sided numerical aperture between 0.27 and 0.33. However, the intrinsic complexity was fairly increased for the recent developments augmenting the number of degrees of freedom and thus increasing the correction abilities for off-axis zones. Numerical evaluations predicted a diffraction-limited imaging within an area of less than 20 μm in diameter for the precursor which could be significantly increased for the two redevelopments to up to 300 μm. In order to achieve this goal, two color correcting concepts were assimilated in the recent developments, firstly by utilizing a diffractive optical element and secondly by using an achromatic lens. A subsequent assembling and experimental evaluation confirmed these numerical predictions and approved a successful development.

The experiments indicated that RePolyC, the device which incorporates an achromatic lens for the color correction, is the best candidate for a further transfer in production if the priority is given to a high sensitivity. However, confocal images observed in fluorescence mode at a subresolution fluorescine layer indicated that DiPolyC, the assembly which incorporates a diffractive optical element, is the adequate candidate if the preferences focus rather on a homogeneous image than on a high peak intensity. Future improvements could focus on the implementation of anti-reflection coatings, especially for the high refractive index elements as well as a further decrease of the induced, uncontrollable aberrations of the GRIN-lens by even better adapting the GRIN-profile to the desired polynomial. In addition, measured diffraction efficiencies of the DOE’s are hardly accessible up to date. Future projects aim on their determination by measuring the diffraction efficiencies at homogeneous gratings with different periods and a consecutive calculation of the overall diffraction efficiency of the desired order by integral methods. This will lead to a better understanding and description of the GRIN-probes.