Field curvature reduction in miniaturized high numerical aperture and large field-of-view objective lenses with sub 1 µm lateral resolution

In this paper the development of a miniaturized endoscopic objective lens for various biophotonics applications is presented. While limiting the mechanical dimensions to 2.2 mm diameter and 13 mm total length, a numerical aperture of 0.7 in water and a field-of-view (FOV) diameter of 282 µm are achieved. To enable multimodal usage a wavelength range of 488 nm to 632 nm was considered. The performed broad design study aimed for field curvature reduction when maintaining the sub 1 µm resolution over a large FOV. Moreover, the usage of GRadient-INdex (GRIN) lenses was investigated. The resolution, field curvature improvement and chromatic performance of the novel device were validated by means of a confocal laser-scanning-microscope.

A state-of-the-art objective lens that fulfils the criteria of a large NA of 0.73, a well-corrected FOV diameter of 264 µm as well as a design spectral range of at least 488 nm to 550 nm already exists (MO-080-032-ACR-VISNIR-08CG-20, GRINTECH GmbH, Jena, Germany) and can be used in a broad range of applications [17].However, to achieve these specifications, a field curvature radius had been tolerated and allowed as an additional degree of freedom in the optical design process.In the past years, more applications have arisen that need for less field curvature or for tailoring of the field curvature to a specific application [18,20].
In the first part of this paper, the set of requirements for the novel device is described.Afterwards, the results of the design process are shown where three different design options are compared.In the last part, the assembled prototypes are evaluated regarding their performance by means of a confocal laser-scanning-microscope.Besides the resolution also the field curvature and the chromatic performance of the miniaturized objective lens are shown.Furthermore, biological cell samples were imaged with the device.

Requirements
The main goal of the performed design study was to develop a novel miniaturized objective lens which reaches a diffraction-limited sub 1 µm lateral resolution when optimizing the optical design for a larger field curvature radius than the state-of-the-art system and thus to reduce the necessary axial focal shift to assess the whole FOV.
The device should occupy as less space as possible to enable especially endoscopic usage and therefore needs to have the smallest possible total volume.For enabling a multimodal usage in a wide spectral range three design wavelengths are considered, 488 nm, 550 nm and 632 nm.A field-of-view (FOV) diameter of at least 264 µm was targeted.For one specific application a fused silica wafer with a thickness of 200 µm needs to be used with an air gap of 50 µm to the miniaturized objective lens.A NA of 0.7 in 20 µm water immersion was aimed for.
The high NA miniaturized objective lens should be able to be used as stand-alone device as well as a relay system.It should be capable of imaging e.g.bacteria and their signal into an intermediate image plane which could also be the object plane of a microscope objective lens.A magnification of the system of 2.2 was targeted which results in a NA towards the image plane of 0.32.Furthermore, it should be aimed for smallest possible deviations from double sided telecentricity.This is necessary on the high NA side for constant magnification when changing the working distance in case of volume acquisitions and to keep the spherical aberration independent of the field height when using cover glasses.Towards the intermediate image plane telecentricity was required for achieving pupil matching with possible following optics e.g. when using the objective lens for NA enhancement and thus as relay.
The combination of high NA, large FOV and small deviations from telecentricity is even more challenging for the requirement of using a mounted diameter of less than 5 mm when not accepting energy losses over the whole FOV.The maximum field height with diffraction limited performance is enhanced by a factor of 1.9 when using a ROC of 2 mm instead of 550 µm.

Relation of field curvature and field-of-view
The effect of accepting a field curvature radius (ROC) of 550 µm is illustrated in Fig. 1 on the left side.When acquiring only one single slice and not allowing for an axial focal shift and considering the Rayleigh range R for the depth-of-focus (DOF) the assessed FOV can be enlarged by a factor of 1.9 by using larger radii of curvature as shown for ROC = 2 mm (Fig. 1 right).

Starting point of the design study
The ROC of 550 µm shown in Fig. 1 corresponds to the accepted residual field curvature radius of a finite-to-finite-corrected miniature objective lens (MO-080-032-ACR-VISNIR-08CG-20, GRINTECH GmbH, Jena, Germany).The specifications of this device are shown in Fig. 2. As almost all specifications except for the field curvature radius are similar to the requirements in the current main application, this design was chosen as starting point for the performed design study and for comparison in the experimental evaluation.The state-of-the-art objective lens type MO-080-032-ACR-VISNIR-08CG-20 is called MO-ACR in this paper.This device can be used with a 170 µm N-BK7 cover glass and a working distance of 80 µm in water.It is a finite-to-finite corrected objective lens and features a NA of 0.73 in water and 0.32 towards the intermediate image plane which yields a magnification of 2.3.The FOV diameter in the sample is 264 µm.It was designed for two design wavelengths, 488 nm and 550 nm.On the high NA side, a deviation from telecentricity of 7°was accepted.Moreover, for achieving a mounted diameter of 1.3 mm an energy loss of 12% at the field edge was tolerated for the underlying applications of this device (Fig. 3).
The spot performance of the device for the three required wavelengths on axis and for 488 nm and 550 nm also for two off-axis points is shown in Fig. 4 left.If the ROC would be changed to 2 mm (Fig. 4 right) the off-axis performance would drop as predicted in Fig. 1.

Design process and results
The optical design of the MO-ACR was used as a starting point for the design study to reduce the field curvature when maintaining the sub 1 µm performance, improving the chromatic behaviour, reducing deviations from double-sided telecentricity and avoiding vignetting effects.In the Merit function of the used software OpticStudio (Ansys, Canonsburg, Pennsylvania, USA) the targeted specifications were demanded.Furthermore, also a distortion monitoring was implemented.For this application the outer dimensions could be increased in comparison to the starting design to 2.2 mm mounted diameter which helped to reach the field flattening and to fully avoid vignetting in the defined FOV.
Besides the requirements also the manufacturability, e.g. the edge and center thickness of the refractive components as well as the Gradient-Index (GRIN) profiles, was already taken into account in the Merit function.To achieve this, more degrees of freedom were required.In addition to the lens shapes, distances between the optical components and the GRIN profile parameters as well as material changes were allowed as degrees of freedom.
GRIN lenses have a great advantage in micro optical systems as e.g.their plane surfaces simplify the assembly significantly and adapting the refractive index profile to the requirements offers appreciated degrees of freedom in the design process [11,21].However, the optimization speed is decreased when using GRIN profile optimization due to the tremendously increased computational effort of the design soft-and hardware.Therefore, also solutions without GRIN lenses were investigated.In general, material changes were the most promising as not only chromatic aberrations but also the Petzval sum can be influenced by changing the glass materials [22,23].For this, a global optimization of the system was performed.However, a preliminary study showed, that also structural changes e.g., adding a lens or splitting a doublet are needed to reach all design goals.16 optical design solutions were worked out.For full field flattening the number of required optical and mechanical elements of the designs needed to be raised.In other designs a slight field curvature was allowed to reduce the number of needed lenses and for further improvement of the performance.The best three optical designs (A, B and C) were shortlisted and investigated in more aspects.The three-dimensional layouts of the designs are shown in Fig. 5.
The nominal RMS spot radius performance for the three design wavelengths and field positions in comparison to MO-ACR is shown in Fig. 6.When comparing the performance of the designs the different allowed field curvature radii of the designs need to be considered as shown in the last column in Fig. 7, respectively.For an easier comparison of the designs the allowed ROC were normalized by the maximum sample field height Y' max for each system For design A, a field curvature radius of 1.5 mm and a maximum sample field height of 0.141 mm were used which equals to a ROC n of 10.64.For design B a field curvature radius of 2 mm and therefore a ROC n of 14.18 were allowed, whereas design C features full field flattening.In comparison to these numbers, MO-ACR was designed with a field curvature radius of 0.55 mm in the sample plane and a maximum sample field height of 0.132 mm which equals a ROC n of 4.17.
Fig. 6.Nominal RMS spot radii in µm for the wavelengths 488 nm, 550 nm and 632 nm of design A-C for three sample field radii.All designs reach for all wavelengths a sub 1 µm lateral resolution.
Besides the RMS spot radius performance Fig. 6 shows the Airy radius for all design wavelengths.In design A the ROC n was improved by a factor of 2.55 in comparison to the state-of-the-art device.It achieves for all wavelengths and field points diffraction-limited RMS spot radii.Design B provides an even larger field curvature correction than design A. As shown in Fig. 1 the maximum field height with diffraction limited performance is enhanced by a factor of 1.9 when using design B instead of MO-ACR.Design C shows the possibility to maintain the spot performance when totally flattening the FOV in comparison with the MO-ACR.Though, a design with more optical and mechanical components is required to reach the flattened FOV.Hence, a larger number of optical components and a larger volume of the system are inevitable.
Figure 6 shows that for all designs a nominal geometrical RMS spot radius performance of sub 1 µm and even for all design wavelengths on-axis and for design A and B for the wavelengths 488 nm and 550 nm also off-axis a 0.5 µm resolution is achieved.

Realization aspects
In a next step the influence of the geometrical and material tolerances of the optical components, the tilt and decenter of the sub-assemblies and the tolerances of the mechanical components on the optical performance of the device was calculated.The sensitivity of the design performance to the single tolerances was investigated.The gained information was used for reoptimizing the systems and to improve the mechanical design concepts.Besides the sensitivity analysis, a Monte Carlo simulation of 50 sample systems was performed [24].The number of systems which still reaches a sub 1 µm spot RMS radius performance when taking the tolerances into account was calculated.The results of the tolerance analysis are presented in Table 1.
Design B showed a lower sensitivity to the tolerances and a higher yield of sample systems than design A und C. Thus, design B was chosen for fabrication.A blackbox file of design B is available in Dataset 1, Ref. [25].The four lenses, the front window and the mechanical components as well as the dimensions of the assembled system in comparison to a match are shown in Fig. 7.
The refractive lenses are all customized lenses of high refractive index materials with a semidiameter of 1.0 mm and 0.9 mm, respectively.Prior to the final assembly two sub-assemblies were built up using high precision laser cut stainless steel tubes.One doublet was mounted into a stainless-steel tube which also provides the correct distancing towards the rod lens in the middle part of the objective lens.For the second sub-assembly one doublet and one singlet together with the front window were mounted in a stainless-steel mount.An intermediate stainless-steel ring was used to keep these components at the needed distance.For the final assembly step the rod lens and the two sub-assemblies were inserted into the outer stainless-steel tube.

Field curvature simulations
For investigating the improvement of the ROC the Strehl ratio for all field points in dependency of the working distance was simulated for MO-ACR and for design B (Fig. 8).The DOF was calculated as double Rayleigh range according to Eq. ( 1).Similar as in Fig. 1 the DOF was drawn as white dotted lines for the on-axis case.
Figure 8 shows that the required working distance change to acquire the whole FOV is reduced for the novel design.Furthermore, the increased peak height of the Strehl ratio shows the improved absolute performance.

Predicted visual perception
To help predicting the performance for extended field areas for the starting design in comparison to the chosen design B an imaging simulation was performed.For this purpose, an 18 µm x 18 µm pattern with smallest structure sizes of 2 µm in the detection plane was used and simulated to be imaged through the optical designs of MO-ACR and the novel device (Fig. 9).
The smallest structure size in the detection plane is smaller than 1 µm when taking the magnification of the objective lenses into account which is smaller than twice the Airy radius for all used wavelengths.Therefore, it equals to the diffraction limit.For the visualization of possible differences in tangential and sagittal direction also longer structures in both directions were introduced in the pattern.Furthermore, it can also simulate the imaging quality for larger structures like strains of bacteria in the lower right part.
For the simulations the tool "extended diffraction image analysis" by OpticStudio was used.With this tool an extended section of the object field can be imaged through the optical system which can help to predict the visual perception through the device for different field positions.
The number of pixels of the object as well as the size of the object field section that is imaged can be chosen.In this example 9 × 9 pixels and a field section of 18 µm x 18 µm were used.The optical transfer function (OTF) is calculated by means of the Fourier transform of the point spread function.In this simulation the OTF is assumed to be constant over the chosen 18 µm x 18 µm field section.The results of the imaging simulations for MO-ACR and the novel design are presented in the lower part of Fig. 9.
The simulations visualize that all imaged structures can be identified as separated for all field positions and wavelengths in both designs.The imaging quality of design B which was designed for an increased ROC by a factor of almost 4 is maintained when comparing to MO-ACR.For the wavelength 632 nm even an improvement for design B was reached.

Experimental validation by means of a confocal laser-scanning-microscope
For assessing the imaging performance of the system for the main design wavelengths 488 nm and 550 nm a confocal laser-scanning-microscope (LSM) was used (FV1000, Olympus EUROPA SE & Co. KG, Hamburg, Germany) (Fig. 10 left).The developed miniature device was aligned in front of a 10 x microscope objective lens with a NA of 0.4 (UPLSAPO10X2, Olympus EUROPA SE & Co. KG, Hamburg, Germany) by means of a micro stage (Pos3X Unit, GRINTECH, Jena, Germany) and a magnetic clamping unit (Fig. 10 right).
The last lens of the miniaturized objective lens was brought into the focal plane and optical axis of the LSM objective lens by using the xyz axes of the micro stage.To reach the correct working distance the z distance of the objective lenses towards each other was increased by means of the z axis of the micro stage.
Two different fluorescent bead samples were prepared.For a robust assessment of the imaging performance 2 µm bead samples were prepared on microscope slides.For the MO-ACR the bead layer was covered with a 170 µm cover glass and a drop of deionized water to simulate the 80 µm working distance in water immersion.The novel device is mainly designed for a 200 µm thick  wafer in combination with a 50 µm air gap.The additional 20 µm working distance in water had to be neglected for this test.Therefore, for testing the novel device the bead layer was covered by a 200 µm fused silica wafer with an air gap between the first lens of the device and the wafer.The distance of the high NA side of the miniaturized objective lens towards the bead layer was adjusted by the z positioning unit of the LSM.The fluorescent beads were excited by a laser wavelength of 488 nm.The Stokes-shifted signal at 540 nm was collected which allows to assess the two main design wavelengths.A voltage of 535 V at the photo multiplier tube (PMT) and a diameter of the confocal pinhole of 80 µm were set.The measured power in the sample plane was 22 µW.
For assessing the whole FOV z stacks of 1 µm distanced slices were acquired for both devices.A resolution of 1024 px x 1024 px and a dwell rate of 10 µs/px were used.As shown in the first row of Fig. 11. for MO-ACR 41 slices were acquired whereas for the novel device only 11 slices were needed.
For both stacks an axial maximum intensity projection was calculated by means of the software ImageJ (Fig. 11, second row).The red rings which correspond to the radius of the outermost field point in the design and therefore indicate the edges of the design FOV, respectively, help to observe that both devices are capable of imaging an even larger FOV than requested in the requirements.The slightly different magnifications of the two devices result in a difference of the FOV diameter which is indicated by the scale bars for the sample planes.The last row of Fig. 11 shows lateral maximum intensity projections of the same image stacks to visualize the difference in field curvature as simulated in Fig. 8.By this, it was possible to show that the first main goal of this work to improve the field curvature radius was achieved.For verification of also the second main goal, the maintenance of the sub 1 µm performance, 200 nm beads samples (FluoSpheres Carboxylate 0.2 µm yellow-green 505/515, 2% solids, diluted 1:500 in deionized water) were produced.Figure 12 shows the maximum intensity projection of a stack consisting of 111 slices which was acquired with a resolution of 1024 px x 1024 px and a dwell rate of 10 µs/px with the LSM.For a better visualization the brightness of the maximum intensity projection shown in the middle of Fig. 12 was adapted.The 50 x zoom function of the LSM was used to assess single beads in sub-areas which were analyzed regarding their full-width at half maximum (FWHM) values.As can be seen in the right graph of Fig. 12 for all 4 field positions FWHM values of 0.5 µm and smaller can be achieved which is in the range of the Airy radius.The slight deviation of the FWHM value for the sample field radius of 141 µm might be most likely explained by measurement tolerances.

Chromatic performance of the system
For assessing the chromatic performance of the system the Strehl ratio was simulated in dependency of the wavelength over a range of 450 nm to 950 nm when allowing for refocussing the working distance (Fig. 13).
For checking the imaging behaviour of the system also for a longer wavelength usage a mixed bead solution consisting of 2 µm diameter beads for two different excitation wavelengths (Polysterene microspheres, color dragon green and flash red; 2,07 µm diameter, Bang laboratories, Indianapolis, Indiana, USA) was prepared.Two laser channels of the LSM were used to acquire two separate z stacks.In Fig. 14 the axial lateral maximum intensity projections of 11 single slices for an excitation wavelength of 488 nm (left) and 660 nm (middle) and their superposition (right) are shown.It can be evaluated that the novel miniaturized objective lens is capable to image 2 µm beads also at the edge of FOV for the third design wavelength.

Imaging of biological samples
Many applications demand imaging of biological structures of bacteria or other cells.Therefore, two different cell samples were imaged with the novel objective lens using the LSM at an   For the sample preparation HEK 293 cells were maintained in a culture medium consisting of Dulbecco's modified Eagle's medium with 4500 mg glucose/L, 110 mg sodium pyruvate/L supplemented with 10% fetal bovine serum, glutamine (2 mM), and penicillin-streptomycin (1%).The cells were cultured at 37°C/8,5% CO 2 and were grown on #1.5 cover glasses.For the labeling of the actin cytoskeleton the actin marker Phalloidin Alexa 488 (Invitrogen, Carlsbad, California, USA) was used according to the instructions of the manufacturer.Peroxisomes are visualized by the expression of the peroxisomal matrix protein SCP2 with a N-terminal eGFP tag.Here the cells were transfected with 500 ng of plasmid DNA (eGFP-SCP2) [27] per dish using Lipofectamine 2000 transfection reagent (Invitrogen, Carlsbad, California, USA).24 h after transfection the cells were fixed with 3% formaldehyde for 20 minutes, washed with PBS and the cover slides were mounted in Mowiol.
For each sample we acquired image z stacks of 578 µm x 578 µm size in the sample plane with 2048 px x 2048 px resolution and a dwell rate of 20 µs/px (Fig. 15).Both stacks consist of 21 slices with an axial step size of 0.5 µm.For the upper part of Fig. 15 a voltage of 484 V was applied at the PMT and for the lower part 410 V.In the first column the maximum intensity projection of the stacks is shown.For each sample two 10 x zoom-areas were acquired which are shown in the middle and right column, respectively.Neither the brightness nor the contrast of these acquired images were adjusted.Even the sub-cellular features were visible which enables the application of this device also in many other biomedical fields.

Conclusion
In the scope of this work the miniaturized objective lens MO-ACR of the company GRINTECH was further developed and tailored to new applications.A broad design study to address all requirements and achieve field curvature improvement when maintaining a sub 1 µm lateral resolution was conducted.The development process also included tolerance analyses, imaging prediction simulations, mechanical concepts and prototype assembly.
We were able to demonstrate the targeted sub 1 µm lateral resolution as well as the field curvature improvement of the novel developed device in simulations.Moreover, this was proved in a performance assessment by using a confocal laser-scanning-microscope to image fluorescent bead targets and biological cell samples.Future work will aim for a respective product development and in addition for complete field flattening, further miniaturization and reduction of components by adapted GRIN lenses.Research (LPI).The LPI initiated by Leibniz-IPHT, Leibniz-HKI, UKJ and FSU Jena is part of the BMBF national roadmap for research infrastructures.
In addition to the co-authors and their continuous support and input, a special thanks to all colleagues at GRINTECH, in particular to Sandra Gerlach-Anhut for the discussions about the LSM measurements and Thomas Raack for help with the assembly process.Furthermore, we thank the project consortium for the productive collaboration.

Fig. 1 .
Fig.1.Relation of the field curvature radius and the usable field-of-view for a ROC = 550 µm (left) and ROC = 2 mm (right) when taking the Rayleigh range for the depth-of-focus into account.The maximum field height with diffraction limited performance is enhanced by a factor of 1.9 when using a ROC of 2 mm instead of 550 µm.

Fig. 3 .
Fig. 3. Energy loss of MO-ACR as transmission in % in dependency of the sample field radius in µm.At the field edge an energy loss of 12% is accepted.

Fig. 4 .
Fig. 4. RMS spot radius performance in µm in dependency of the sample field radius in µm for the MO-ACR for a field curvature radius (ROC) in the sample plane of 0.55 mm (left) and 2 mm (right).

Fig. 5 .
Fig.5.Three dimensional layouts of MO-ACR and the three design options with the allowed field curvature effects.For MO-ACR the scale bar corresponds to 1 mm and for the other designs to 2 mm, respectively.Below the layout the used lens combination is listed.

Table 1 .Fig. 7 .
Fig. 7. Optical and mechanical components for the objective lens (right).Assembled miniature objective lens next to a match (left).The scale bars correspond to 5 mm, respectively.

Fig. 8 .
Fig. 8. Strehl ratio in dependency of the working distance change in µm and the normalized sample field position for the central design wavelength 550 nm for MO-ACR (left) and the novel design (right).The shown normalized field-of-view equals to 132 µm field radius for MO-ACR and to 141 µm for design B, respectively.A similar figure was presented also in [26].

Fig. 9 .
Fig. 9. Scheme for the imaging simulations by the optical designs.For each field height a 18 µm x 18 µm pattern with structure sizes of 2 µm was imaged through the optical system (top).The scale bar corresponds to 2 µm in all shown simulations.Imaging results for MO-ACR (left) and for design B (right) for all design wavelengths and three sample field positions.

Fig. 10 .
Fig. 10.Confocal laser-scanning-microscope (LSM) (left).Adjusted LSM setup with micro stage and clamping unit for positioning and aligning the miniaturized objective lens in front of the LSM objective lens (right).

Fig. 11 .Fig. 12 .
Fig. 11.First row: Acquired z stack with 2 µm beads for MO-ACR (left) and design B (right).For assessing the whole field-of-view a stack of 40 µm with slice distance of 1 µm was acquired while for design B 11 slices where required.Second row: Axial maximum intensity projection for MO-ACR (left) and design B (right).The white scale bars correspond to 200 µm in the intermediate image plane between the miniaturized objective lens and the objective lens of the laser-scanning-microscope. The red values correspond to the same scale bar in the sample plane.The red circle corresponds to the diameter of the maximum design position.For MO-ACR the diameter is 264 µm in the sample plane and for design B 282 µm.Third row: Lateral maximum intensity projection for MO-ACR (left) and design B (right).

Fig. 13 .Fig. 14 .
Fig. 13.Strehl ratio of the novel design in dependency of the wavelength in nm when allowing for a working distance change in µm.

Fig. 15 .
Fig. 15.HEK 293 cells stained with the actin dye Phalloidin Alexa 488 (upper row) or expressing the peroxisomal matrix protein eGFP-SCP2 (lower row) imaged with the new objective lens in front of a confocal laser-scanning-microscope (LSM).The scale bars in the left column correspond to 200 µm in the intermediate image plane and to 91 µm in the sample plane, respectively.Next to the full field-of-view maximum intensity projections of 10 µm stacks zoom-areas of the marked areas in the first column are shown.These were acquired using the 10 x zoom of the LSM.Therefore, the scale bars of the zoom-areas correspond to 20 µm in the intermediate image plane and to 9.1 µm in the sample plane, respectively.