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Abstract
The investigation of deep-sea microorganisms holds immense significance and value in advancing the fields of life sciences, biotechnology, and environmental conservation. However, the current lack of specialized underwater objectives specifically designed for in situ studies of deep-sea microorganisms hampers progress in this area. To address this limitation, we present the design of a multi-band Raman tweezer objective tailored for deep-sea environments. The objective is integrated into a high-pressure chamber capable of withstanding depths up to 1.5 km, enabling in situ microscopic imaging, optical tweezer capture, and Raman detection of deep-sea microorganisms. Through meticulous structural optimization, meticulous material selection, and thorough mechanical analysis of the underwater optical window, the objective exhibits remarkable attributes such as multi-band functionality, extended working distance, and high numerical aperture. Our design yields image quality near the diffraction limit, successfully achieving flat-field and apochromatic performance in each respective wavelength bands. Moreover, the tolerance analysis demonstrates that the full-field root mean square (RMS) wave aberration approaches λ/14, effectively meeting the demands of manufacturing and practical applications. This objective lens constitutes a vital tool for the in situ exploration of deep-sea microorganisms.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The deep sea, which refers to the oceanic areas with depths below 1,000 meters, represents the largest and least explored habitat on our planet. Encompassing over 50% of the ocean's surface, it holds immense biological resources and energy. Investigating microorganisms within the extreme conditions of the deep sea can unveil the physiological and biochemical characteristics of these organisms, as well as shed light on their origins. This knowledge can then pave the way for the discovery of unique genes and products with significant applications in various fields, including industry, pharmaceuticals, economy, energy, and ecology [1,2].
Significant advancements have been achieved in deep-sea microbial research [3,4], yet numerous challenges persist. Presently, the analysis of deep-sea microorganisms requires their capture in seawater and subsequent transportation to land for further investigation. Unfortunately, the unique attributes of the deep-sea environment lead to irreversible alterations in microorganisms once removed from their natural in situ habitat. The proportion of uncultivable deep-sea microorganisms may even surpass 90% within traditional laboratories [5]. Thus, a prominent challenge lies in the absence of specialized instruments for in situ deep-sea microbial research [6,7]. Moreover, the study of deep-sea microorganisms encounters additional difficulties encompassing specimen collection, cultivation, species identification, and data analysis [8,9]. Zhang utilized Raman probes to acquire high-quality Raman data for substances like pore waters and natural gas hydrates from the seafloor [10]. However, Raman probes themselves lack microscopic imaging capabilities and are unsuitable for deep-sea microbial detection. Liu developed an integrated device that combines microscopic imaging and Raman detection functionalities, mounted on a remotely operated vehicle (ROV), enabling imaging and Raman analysis of deep-sea targets at depths of 770 meters. This led to a wealth of images and Raman spectra pertaining to targets such as starfish and shells [11]. Nonetheless, the system's microscopic objective has limited resolution, rendering it inadequate for observing and detecting deep-sea microorganisms, and it cannot capture these microorganisms. Mullen proposed an underwater microscope for in situ deep-sea research, achieving a resolution at the micrometer level and capturing clear images of coral polyps [12]. Nevertheless, this apparatus is only suitable for shallow-sea seabed operations and cannot realize Raman detection and capture of microorganisms.
Overall, the existing deep-sea imaging and detection instruments have yet to simultaneously address the high-resolution microscopic imaging and Raman detection capabilities. Typically, more destructive mechanical arms are employed for capturing seabed targets, often larger in size, and a superior approach for capturing small microorganisms in marine water is currently lacking.
To overcome the aforementioned challenges in the study of deep-sea microorganisms, this thesis presents the design of a multi-band microscope objective specifically tailored for deep-sea high-pressure environments. This objective serves a dual purpose, enabling in situ imaging and observation of deep-sea microorganisms, as well as functioning as an integral component of a Raman optical tweezers system, thereby addressing the lack of a dedicated microscope for deep-sea applications. Raman tweezers seamlessly integrate the contactless, low-damage, and high-precision capabilities of optical tweezers with the rapid, label-free, and non-destructive attributes of Raman spectroscopy [13,14], Consequently, this combined approach enables the in situ sorting and detection of deep-sea microorganisms.
The deep-sea objective developed in this study serves as a sub-module within the deep-sea microbial in situ sorter equipment. It is specifically designed for installation in a pressure-resistant chamber capable of operating at depths of up to 1.5 km. To facilitate stable three-dimensional capture traps and optimize the collection of Raman scattered light, both optical tweezers and Raman detection demand an objective with high numerical aperture (NA) and excellent transmittance [14–16]. Light sources centered at 550 nm, 1064 nm and 785 nm are used in the three subsystems of the sorter - imaging, tweezers, and Raman. Since these three subsystems share a common objective lens, it is imperative that the objective lens demonstrates excellent imaging quality across all three wavelength bands.
Figure 1 depicts the schematic diagram of the objective lens functioning within the deep-sea environment. To achieve waterproof sealing, a thick underwater pressure-resistant window is positioned between the objective lens and the seawater outside the chamber. On the outside of the underwater optical window is a microfluidic chip for in situ sorting of deep-sea microorganisms. The chip is immersed in seawater. The laser beams from the tweezer and Raman systems converge through the objective lens, traverse the underwater optical window, seawater, and ultimately focus on the microfluidic channel of the microfluidic chip. This enables optical tweezer capture and Raman spectroscopy detection of deep-sea microorganisms. Consequently, the objective lens must possess a sufficiently long working distance while ensuring a high numerical aperture.
In this study, combined with the low temperature and high-pressure characteristics of the deep-sea environment, the aberration correction of underwater windows and seawater media was considered. Through structural analysis and design, pressure analysis and reasonable selection of glass material combination, the optical design software OpticStudio was used to design a multi-band Raman tweezer objective lens suitable for deep-sea environment, with 33x magnification, 0.8 numerical aperture and 6.1 mm working distance, and flat-field apochromatic function. Finally, the objective lens is assigned and analyzed for tolerances.
2. Preliminary consideration
2.1. Design details of the multi-band Raman tweezers objective
When designing objectives for Raman testing, it is essential to consider the following requirements: (a) High resolution: The objective should possess excellent imaging capabilities to achieve sub-micrometer level resolution, ensuring the detailed examination of microorganisms and structures. (b) High numerical aperture: A high numerical aperture is crucial for enhancing the collection of weak signals, improving the sensitivity of Raman detection, and enhancing the signal-to-noise ratio. (c) Low autofluorescence: To ensure accurate Raman spectroscopy test results, the objective should exhibit minimal autofluorescence to avoid any interference with the detected signals. (d) High transmittance: The objective lens should provide high transmission efficiency to ensure optimal Raman signal transmission. During Raman detection, it is necessary to select an appropriate excitation wavelength based on specific experimental requirements and sample characteristics. The intensity of scattered light is inversely proportional to the fourth power of the excitation wavelength [17]. While 532 nm excitation light offers stronger Raman signals and higher spatial resolution, it is accompanied by higher fluorescence background and increased photodamage. On the other hand, 1064 nm near-infrared excitation light experiences less fluorescence interference and enables more accurate Raman signal detection. Furthermore, it imposes less damage on microorganisms and exhibits greater penetrating power. However, most detectors utilize silicon-based CCD chips that are unresponsive to light above 1100 nm, and their quantum efficiency is low [18]. As a balanced option, the 785 nm excitation light offers performance characteristics between 532 nm and 1064 nm. It is widely used, exhibits low phototoxicity to cells [19,20], and is suitable for detecting deep-sea microorganisms. Thus, the instrument employs a 785 nm laser as the Raman excitation light and is equipped with a 1200 g/mm grating, enabling a spectral detection range of 200 - 2000cm-1, corresponding to a Raman scattered light wavelength range of 797 - 931 nm. Consequently, the objective's red-optimized wavelength band should encompass the 797 - 931 nm band with a central wavelength of 785 nm.
The objective used for optical tweezers requires a high numerical aperture (NA) to effectively converge the beam. High NA objective lenses enable Gaussian beams to generate an optical field with intense gradients at the focal point, creating a stable three-dimensional optical trap [15,16]. In optical tweezers, the most commonly used laser wavelength is 1064 nm, as near-infrared laser wavelengths pose lower damage to microorganisms confined in the optical trap [21,22]. However, general objectives are typically optimized for visible wavelengths and need further optimization for near-infrared wavelengths around 1064 nm.
Figure 2 presents a schematic diagram of the objective lens assembly integrated with the flange cover of the high-pressure chamber. To protect the optical system from the pressure of seawater, underwater imaging equipment is typically installed in an atmospheric pressure chamber. In this instrument, a high-strength and corrosion-resistant titanium alloy is employed to manufacture the high-pressure resistant chamber and flange. The underwater optical window, made of sapphire glass with a Mohs hardness of 9, exhibits remarkable characteristics such as high-pressure resistance, scratch resistance, and resistance to acid and alkali corrosion. Sapphire glass is widely used as a protective window for deep-water cameras. It possesses high transmittance across the UV to IR band, with near-infrared transmittance exceeding 85% for 2-4 mm thick sapphire plates at room temperature [23]. Hence, it is an ideal material for underwater optical window. Microfluidic chips, on the other hand, utilize quartz glass due to its low fluorescence background in the near-infrared (NIR) spectral range, as well as its high transmittance and corrosion resistance [20]. The microfluidic chip is securely positioned in a stainless steel fixture adjacent to the underwater optical window, with seawater filling the space between the two underwater optical windows. The system employs focused transmission illumination for microscopic imaging.
Within the constraints of standard sizes, objective lenses are available in flush-focus lengths of 95 mm, 60 mm, and 45 mm. However, it is often challenging to achieve both high NA and long working distance in the same objective due to their inherent trade-off. High NA objectives typically have a shorter working distance. To satisfy the requirements of high NA and long working distance, the back focal length ($f$) of the objective lens should be increased, and the aperture ($D$) of the entry pupil should be relatively larger, as indicated by the numerical aperture Eq. (1) [24]. After optimizing the objective structure, it was determined that a working distance of ≥ 6 mm meets the practical needs. At this working distance, the net diameter of the underwater optical window at the front of the objective is approximately 10 mm. Considering the thickness of the mechanical housing, the through-aperture of the underwater optical window was set at 15 mm, corresponding to the through-aperture of the flange.
The objective designed in this study is a water immersion objective for multi-band Raman optical tweezers. It follows the Abbe type objective structure. Through consultation of patents and lens manuals, an Abbe type objective with similar parameters was chosen as the initial structure. Further modifications were made, including lens addition, focal length scaling, band widening, and glass material replacement.
To meet the deep-sea microorganism in situ sorter's needs, the objective lens must adhere to specified design criteria listed in Table 1. These criteria include ensuring a flat field and apochromatic performance. After tolerances are allocated, the RMS wavefront aberration across the full field should approximate the Marechal criterion [25], which sets the requirement that this aberration must be less than λ/14, with distortion controlled within 1%.
Table 1. Design indicators of multi-band optical tweezers Raman objectives
aThe resolution sizes were determined based on the Rayleigh criterion (0.61λ/NA) for different spectral bands. In the imaging band, λ is 550 nm; for the optical tweezers band, λ is 1064 nm; and in the Raman band, λ is 785 nm.
2.2. Static analysis of underwater optical windows
The underwater optical window holds significant importance in ensuring the waterproof performance of the entire device. As seawater pressure changes, the shape of the underwater window undergoes deformation, subsequently affecting the imaging quality of the objective lens. Therefore, conducting finite element static analysis on the underwater window is essential to calculate its maximum deformation and maximum equivalent stress, ensuring its safety. The deformed shape of the compressed window surface was then imported into OpticStudio for aberration optimization.
Figure 3 illustrates two common types of underwater windows: the dome type and the flat type. Each type possesses its own advantages and disadvantages. The spherical window boasts higher pressure-bearing capacity and can eliminate distortion when the center of curvature aligns with the center of the pupil. However, the first lens of the objective is typically a hemispherical or curved-moon positive lens, while the spherical window acts as a negative lens, which hampers the objective's focus and flat field correction. Additionally, achieving high processing accuracy for spherical windows proves challenging, making their processing and assembly more difficult. Conversely, the flat window offers a simpler structure, making it easier to process and install. The optical focus of the flat window is 0, and its aberration characteristics are less affected by changes in the refractive index of seawater outside the window. This convenience facilitates the design and optimization of the optical system. However, flat optical windows are prone to issues such as chromatic aberration, increased distortion, and loss of field-of-view [26,27].
In consideration of objective optimization simplicity and lens processing difficulty, the objective lens designed in this study adopts the commonly used flat window structure. While ensuring the pressure resistance of the window, efforts were made to minimize the thickness of the flat plate to reduce the aberration introduced by the parallel plate. The results of the finite element static analysis indicate that the underwater window with a thickness of 2 mm achieves a safety factor of 1.87 at a maximum depth of 1.5 km, surpassing the commonly used safety factor of 1.5. Hence, this thickness is deemed a more suitable choice.
Since an adjustable air gap exists between the objective body and the underwater optical window, the analysis focuses solely on the flange and the underwater optical window, with no involvement of the objective in the force analysis. Figure 4 illustrates the mesh division profiles of the flange cover and the underwater optical window, along with the fixed and force surfaces of the model. The accuracy of the simulation calculation results is influenced by the density and quality of the mesh cells. This model has 1,368,940 elements and 2,263,121 nodes, and the average element quality is 0.80, surpassing the required value of 0.75, indicating satisfactory mesh. A uniform pressure load of 15 MPa was applied to the 15 mm diameter, 2 mm thick sapphire glass surface and the flange cover to simulate the pressure of seawater at a depth of 1.5 km, as shown in Fig. 4(c).
Figure 5 presents the total displacement and equivalent stress clouds of the flange cover and the underwater optical window. The simulation results reveal that at a maximum depth of 1.5 km, the underwater optical window experiences a maximum equivalent stress of 280 MPa and a maximum deformation of 0.0445 mm. Experimental testing demonstrates that the bending strength of the underwater optical window is 523 MPa, resulting in a safety factor of 1.87, surpassing the common safety factor value of 1.5. Additionally, the maximum equivalent stress value of the titanium alloy flange cover is 145.07 MPa, considerably lower than the bending strength value of the flange cover (900 MPa).
Fig. 5. (a) - (b) total displacement cloud and equivalent stress cloud of sapphire flat glass. (c) - (d) total displacement cloud and equivalent stress cloud of flange.
Utilizing the axial displacement cloud data of the underwater optical window, the polynomial aspheric equation for the window is calculated through the polynomial fitting method. Equation (2) represents the derived expression, with a sum of squares error (SSE) value of 4.23*10−8 (mm2), indicating a highly effective fit:
Subsequently, the grid sag surface type in OpticStudio is employed to describe the underwater optical window's surface. This process calculates the sag (z), the partial derivative of z with respect to x, the partial derivative of z with respect to y, and the cross derivative of z at each grid point by defining the number of grid points on the surface of the lens in the x and y directions. These calculated data at all grid points are then arranged in a table in a certain format, and finally the table is imported into the surface properties of the underwater optical window. The sag data points are smoothly interpolated using the Bicubic spline algorithm. Figure 6 illustrates the surface sag of the sapphire underwater optical window at a depth of 1.5 km below sea level.
The objective lens should fulfill the design requirements not only for imaging quality at the maximum depth of seawater but also for maintaining performance close to the design specifications at other depths. Table 2 presents calculations of the maximum equivalent stress values and maximum deformation of the underwater optical window at depths of 0.5 km, 1 km, and 1.5 km.
Table 2. Maximum deformation and maximum equivalent stress of underwater optical window at different seawater depths
Next, the steps of the above analysis were repeated, and the data of the axial displacement cloud was fitted to obtain the aspheric equations of the underwater optical window at these two depths after compressive deformation, based on the results of the finite element static analysis of the submerged light window at the other two depths. Then, the surface type of grid sag in OpticStudio is used to bring the fitted polynomial aspheric surface into OpticStudio for aberration optimization to obtain the optimized structural parameters of the objective at the three depths.
2.3. Establishment of the refractive index model of seawater
The refractive index of seawater is influenced by various parameters such as pressure, temperature, and salinity. However, the currently available glass library lacks materials for deep seawater, and only materials for surface seawater at room temperature and pressure are available. Therefore, it is necessary to establish a seawater refractive index model that can optimize the aberration of the objective lens more accurately in line with the actual deep-sea environment.
In current studies, the widely used Millard and Saver (MS) equation [28] is employed to model the refractive index of seawater. This empirical equation utilizes a least squares regression (LSR) approach to analyze and model multiple sets of measured seawater data. It has been observed that the predicted values from the MS equation align well with experimental measurements within the acceptable error range [29]. The MS seawater refractivity equation incorporates four variables: wavelength, temperature, salinity, and pressure. Pressure can be determined using a simple depth-pressure relationship, while data on seawater temperature and salinity are obtained from the CTD temperature and salinity observation dataset of the South China Sea Marine Science Cross-sectional Expedition [30]. For our study, we extracted seawater temperature and salinity data at depths of 0.5 km, 1 km, and 1.5 km from all stations within the region of 18.009 °N to 17.992 °N and 119.336 °E to 116.995 °E in the South China Sea. It is important to note that seawater temperature at a given depth can exhibit slight variations due to solar thermal radiation, seasonal changes, and interannual variability. To minimize measurement errors and the influence of seasonal variations, we calculated the average values of temperature and salinity at these three depths for all stations within the region from 2009 to 2012. The mean values of seawater temperature and salinity at these depths are presented in Table 3.
Table 3. Average temperature and salinity at different sea depths in the waters near 18° N in the South China. Sea, 2009-2012
The mean values of seawater temperature, salinity, and pressure at depths of 0.5 km, 1 km, and 1.5 km were utilized in the MS seawater refractive index equation to calculate the refractive index of seawater for various wavelengths of light at each location. Subsequently, the calculated values of wavelength and refractive index were fitted using the Schott dispersion equation, resulting in the creation of seawater materials specifically for depths of 0.5 km, 1 km, and 1.5 km. The Schott formula, as shown in Eq. (3) [31]:
The dispersion curves of the seawater medium at the three positions of 0.5 km, 1 km and 1.5 km are shown in Fig. 7. The findings indicate remarkable similarity in the shapes of the three curves, which exhibit relatively shallow slopes and minor dispersion. Computed via the Abbe number formula (Eq. (5)), the Abbe number for all three types of seawater media exceeds 55 within the visible light range (F-D-C wavelengths). As the depth of seawater increases, the refractive index curve of seawater exhibits an overall upward shift, accompanied by an increase in refractive index.
Fig. 7. Seawater medium dispersion curves at various seawater depths. Where SEAWATER, 5MPA_SEAWATER, 10MPA_SEAWATER, and 15MPA_SEAWATER, respectively, represent surface seawater, seawater at 0.5 km, 1 km, and 1.5 km.
3. Objective optimization method
Considering the non-continuous nature of the objective's three working bands and the differing NA and field of view sizes of the imaging and Raman tweezers, we partition the objective into three configurations based on their respective functionalities: imaging, tweezers, and Raman. This division facilitates the optimization of the objective's aberrations. Configuration 1 operates within the wavelength range of 500 - 600 nm, with a center wavelength of 550 nm. Configuration 2 operates within the wavelength range of 1040 - 1090 nm, with a center wavelength of 1064 nm. Lastly, Configuration 3 operates within the wavelength range of 730 - 931 nm, with a center wavelength of 785 nm. Within the multi-configuration editor, each configuration is assigned specific wavelength ranges, NA values, and field of view sizes. It is note that while the imaging system operates in an air medium within the sealed chamber, the target object resides in the seawater medium. Refraction of imaging light through the seawater-underwater optical window-air interface can cause focusing errors, field of view loss, distortion, and chromatic aberrations. Consequently, the underwater optical window, seawater, and microfluidic chip substrate, must be incorporated into the objective lens's aberration optimization process.
The objective optimization scheme can be summarized as follows: First, to meet the practical manufacturing requirements of the objective lens, control over the edge thickness of the positive lens, center thickness of the negative lens, and air spacing is necessary. Specifically, the lens should have a minimum center thickness of 1 mm, a minimum edge thickness of 0.6 mm, and a minimum air spacing of 0.1 mm. Subsequently, throughout the optimization procedure, fundamental parameters of the control system were managed employing Zemax operands. These encompassed the aperture size regulated by the APER control, the effective focal length under the purview of EFFL control, the overall length guided by the TOTL control, and the operational distance governed by the TTGT control. Additionally, to minimize the axial chromatic aberration that occurs after focusing at different wavelengths, we have selected glass materials with partial dispersion that is approximately equal and a large difference in Abbe numbers to construct the secondary spectrum of the glued lens correction system, based on the theory of apochromatic optical system [32]. During the optimization process, the axial chromatic aberration operand AXCL is used to control the axial chromatic aberration in the 0.707 aperture band. Finally, upon obtaining the desired structural parameters that meet the specifications, the tolerance sensitivity operator TOLR is employed to further optimize the aberrations while simultaneously reducing the system's sensitivity to tolerances. This optimization approach facilitates the fulfillment of tolerance requirements without overly constraining the tolerance range, thereby alleviating challenges in the manufacturing and assembly of optical components and reducing overall production costs. In comparison to the conventional optical system design method, which involves aberration optimization followed by tolerance analysis, the design approach in this paper avoids the problem that the actual performance is significantly lower than the nominal performance due to the over-sensitivity of the system to tolerances in the second step of tolerance analysis.
For a wide-spectrum optical system with three bands, correcting the chromatic aberration poses a challenge. The goal of our objective chromatic aberration correction is to satisfy the apochromatic requirement within the sub-bands and to reduce the chromatic aberration between the sub-bands as much as possible. Using the center wavelength of each of the three bands as the system's short-wave wavelength (${\lambda _\textrm{s}}$ =550 nm), middle wavelength (${\lambda _m}$ =785 nm), and long-wave wavelength (${\lambda _l}$ =1064 nm), the secondary spectrum can be described as follows [32]:
The Eq. (4) demonstrates that correcting secondary spectra requires the partial dispersion of glass to be equal and the Abbe number of the glass to be significantly different. However, finding glasses that perfectly meet these requirements is challenging in practice. To maximize the realized apochromatic requirement, it is necessary to select glass materials with similar partial dispersion values while maximizing the difference in Abbe numbers. The lens utilizes a combination of H-ZLAF71 and CAF2 doublet lens, as well as a combination of CAF2, H-TF8, and CAF2 triplet lens for achromatic optimization. The dispersion characteristics of these three glasses are summarized in Table 4, with H-TF8 and H-ZLAF71 sourced from the CDGM glass library, alongside CAF2 hailing from the MISC glass library. The partial dispersion of the three glasses differed very little, and the Abbe number of CAF2 and the other two glasses diverged considerably, meeting the specifications of chromatic correction for the glass materials, as indicated in Table 4.
Table 4. Dispersion characteristics of CAF2, H-TF8 and H-ZLAF71
Furthermore, in order to achieve a apochromatic design, the maximum chromatic focal shift of the objective lens should be less than half of the depth of focus, and an objective lens with a large depth of focus can not only obtain more depth information of the sample [33], but also improve the axial capture efficiency of optical tweezers [34,35]. The objective's depth of focus can be determined using the following Eq. (6) [36], where λ represents the central wavelength of each configuration. According to the equation, the depth of focus for objective configuration 1 is calculated as 2.96 µm, for configuration 2 it is 2.21 µm, and for configuration 3 it is 1.65 µm at a seawater depth of 1.5 km.
4. Results and discussion
4.1. Optical performance
The ultimate optimized configuration of the objective is depicted in Fig. 8. Comprising 8 lens groups (L1 - L8), the objective lens incorporates one doublet lens (L3) and one triplet lens (L4) to achieve apochromatic performance. Notably, the lens L6 and L8 are fashioned from infrared fused silica glass with low Raman background. The objective lens structure parameters are summarized in Table 5.
Table 5. Lens prescription of the Raman tweezers objective
In this study, various evaluation methods were employed to comprehensively assess the objective lens performance. These methods encompass RMS spot radius, modulation transfer function (MTF) curves, diffraction encircled energy, field curvature distortion, chromatic aberration curves, wavefront aberration, and Strehl ratio.
By examining the spot size of the system, one can visually ascertain whether the system has achieved diffraction-limited performance. Table 6 provides a statistical comparison between the maximum RMS Spot Radius of the objective at full field of view and the minimum resolution size of the objective (i.e., the Airy spot radius) calculated in Table 1. The results consistently indicate that the maximum RMS Spot Radius for each objective lens configuration, within the full field of view, is smaller than the Airy spot radius. This confirms that the objective lens achieves the designated resolution criteria.
Table 6. Maximum RMS Spot Radius and Airy Spot radius in full field of view
Figure 9(a) - (c) illustrates the MTF curves of the three configurations of this objective lens. The results demonstrate a maximum cut-off frequency of 2300 cycles/mm. The MTF curves of the three configurations, both in the tangential and sagittal directions, closely approach the diffraction limit, indicating excellent imaging performance of the objective. Both optical tweezers and Raman spectroscopy necessitate a minute, tightly focused spot that possesses concentrated energy and a high gradient force light field. This is essential for achieving stable three-dimensional capture and maximizing Raman signal intensity. Consequently, the energy concentration within the objective's focal spot assumes paramount importance in optical tweezers and Raman experiments. Figure 9(d) - (f) illustrates the diffraction encircled energy curves in the image plane. It is evident from the figure that over 90% of the diffuse spot's energy is concentrated within an energy circle with a 1.5 µm radius, signifying a high energy concentration. This characteristic is expected to have a better capture efficiency and stronger Raman signal intensity for microorganisms larger than 1.5 µm in radius.
Fig. 9. MTF curves and diffraction encircled energy of three configurations of multiband optical tweezers Raman objective. (a) - (c) are the MTF plots of configuration 1 - configuration 3. (d) - (f) are the diffraction encircled energy curves of configuration 1 - configuration 3.
Figure 10 presents the field curves and distortion of the objective lens in the three different configurations. The colored lines in Figs. 10(a)-(c) depict field curves in both tangential and sagittal directions for five different wavelengths of light in each configuration. As illustrated in the figures, the field curvature remains below 1 µm for all wavelengths across the three spectral bands of the objective lens at the maximum field of view. Furthermore, Fig. 10(d) - (f) indicate that the distortion at the edge of the objective's field of view is below 0.02%. As per the ISO international standard for microscopy, a flat field condition necessitates that the absolute values of the average image surface distance ($\varDelta \; $) and astigmatic difference of the objective lens are smaller than the depth of focus. Equation (7) represents this condition [37]:
In the equation, $|\varDelta |\; $ is calculated as shown in Eq. (8):
Fig. 10. Field curvature and distortion plot of three configurations of multiband optical tweezers Raman objectives. (a) - (c) are the field curvature plots of configuration 1 - configuration 3. (d) - (f) are the distortion plots of configuration 1 - configuration 3.
Here, $\tau_{\mathrm{s}}$ and $\tau_{\mathrm{t}}$ represent the distances from the sagittal image surface and the tangential image surface, respectively, to the ideal image plane at the maximum field of view along the direction of the optical axis of the meridian plane. The equation δ calculates the depth of focus in the image space using Berek's formula [34]. Since the result obtained by Berek's formula exceeds that of Eq. (6), the depth of focus value derived from Eq. (6) is used here. Table 7 provides the values of Δ, depth of focus, and image dispersion for the objective lens configurations 1 to 3. It is evident from the table that the absolute values of Δ and astigmatic difference for all three configurations are smaller than the depth of focus, thus satisfying the flat field condition.
Table 7. Depth of focus(δ), and astigmatism of objective lenses
Figure 11 depicts the longitudinal aberration graph and lateral aberration graph of the objective lens. Subfigures (a) - (c) displays the longitudinal aberration curves for the three configurations of the objective lens. In the figure presented, it is evident that the maximum chromatic focal shift for both configuration 1 and configuration 2 is significantly smaller than half of their respective depth of focus. Similarly, the maximum chromatic focal shift of configuration 3 within 90% of the aperture is less than half of the depth of focus. These findings confirm that the objective lens meets the apochromatic specifications. Subfigures (d) - (e) present the lateral aberration curves of the objective. The color light within each configuration falls within the diffraction limit, indicating well-corrected vertical chromatic aberration.
Fig. 11. Longitudinal aberration diagram and lateral aberration diagram of the three configurations of the objective lens. (a) - (c) are the longitudinal aberration maps of configuration 1 - configuration 3, and (d) - (f) are the lateral aberration maps of configuration 1 - configuration 3.
Table 8 presents the RMS wavefront and Strehl ratio at different fields of view for each of the three configurations. The results demonstrate that the RMS wavefront difference is below λ/14 for the majority of fields of view, and the Strehl ratios exceed 0.9 at each field of view for all configurations. These results indicate the excellent imaging quality of the objective. In summary, the objective satisfies the flat field and apochromatic conditions, with the RMS wavefront aberration across the full field of view approaching λ/14, meeting the design specifications.
Table 8. Wavefront and Strehl radio
Furthermore, the objective for deep-sea applications must perform well not only at the maximum depth of 1.5 km but also at other seawater depths to enhance its practical applicability. In this study, the designed objective lens compensates for aberrations caused by changes in the refractive index of seawater and the shape of the underwater optical window at different depths by adjusting the distance between the objective lens and the underwater optical window (the thickness of surface 16) while keeping other structural parameters constant. Table 9 presents the variations in the thickness of surface 16 of the objective at different sea depths: 1 km, 0.5 km, and 0 km. Within Supplement 1, Fig. S1 presents the MTF profiles for the three objective lens configurations at sea level (0 km), Fig. S2 displays the MTF profile at a depth of 0.5 km, and Fig. S3 illustrates the MTF profile at a depth of 1 km. The results indicate that the objective lens maintains good imaging quality at these depths. Therefore, it can be reasonably inferred that by fine-tuning the spacing between the objective lens and the underwater optical window, the imaging quality of the objective lens can still meet the design requirements at other depths.
Table 9. Changes in surface thickness 16 at different seawater depths
4.2. Tolerancing analysis
For optical systems with large apertures and small fields of view, such as microscope objectives, the allocation of tolerances plays a crucial role in determining the final imaging quality and manufacturing cost. Tolerances in optical systems originate from factors such as machining, assembly, and material properties. In the case of optical systems with imaging quality close to the diffraction limit, the RMS wavefront aberration is an appropriate criterion for tolerance analysis.
Initially, more lenient initial values were assigned to each tolerance parameter. Subsequently, the compensator for sensitivity analysis was chosen to be the near-axis focal point, specifically the back focal length. Table 10 presents the four most influential tolerance types on imaging quality, as determined by the tolerance sensitivity analysis. From Table 10, it is evident that the tolerance related to air spacing thickness on surface 16 exerts the most significant influence on system imaging quality. This phenomenon arises from the fact that the front group of the objective lens carries the majority of the system's optical power and is the most sensitive part of the entire system. Consequently, the air spacing thickness of surface 16 is designated as the thickness compensator for system. Additionally, the tolerance range for thickness and decentration is tightened, and the tolerance analysis is continued until the tolerance requirements are met. The final tolerance allocation of the system is shown in Table 11.
Table 10. The most sensitive tolerance types
Table 11. Tolerances for material, manufacturing and alignment
Referring to the manufacturing tolerance levels detailed in Ref. [38], it becomes clear that most of the tolerances in this system adhere to precision standards. Notably, only the component thickness tolerance demands high precision, ensuring the feasibility of actual machining and assembly.
Subsequently, 500 Monte Carlo tests are performed based on the tolerance allocation provided in Table 11. The results, presented in Table 12, indicate that in 90% of the Monte Carlo tests, the RMS wavefront differences for all three configurations are around λ/14, thereby satisfying the tolerance requirements.
Table 12. Result of Monte Carlo tolerance analysis
5. Conclusion
In the absence of dedicated equipment such as a deep-sea microscope objective, the current ability to conduct in situ identification, sorting, and analysis of microorganisms in deep-sea environments is limited. Addressing this need, this study presents the design of a multi-band optical tweezer Raman microscope objective specifically tailored for deep-sea hyperbaric chambers. The objective designed in this paper possesses key characteristics such as high pressure resistance, high numerical aperture, long working distance, and multi-band capability, enabling imaging, optical tweezer capture, and Raman spectroscopy of microorganisms in seawater at depths of up to 1.5 km.
The results of the objective lens design demonstrate the successful achievement of a flat-field and apochromatic design within the three wavelength bands of 500 nm - 600 nm, 730 nm - 930 nm, and 1040 nm - 1090 nm. The optical imaging quality closely approaches the 0.07diffraction limit and satisfies the design requirements. Moreover, through meticulous tolerance optimization and careful compensator selection, the results of tolerance allocation indicate that the objective lens exhibits a full-field RMS wavefront aberration close to λ/14 in each wavelength band, successfully meeting both tolerance requirements and practical processing and production conditions. The design of this objective lens presents a significant advancement, offering a crucial tool for the in situ study of deep-sea microorganisms.
Funding
Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences (No. XDA22020403).
Acknowledgments
This research was financially supported by the Strategic Priority Research Program of the Chinese Academy of Sciences. We acknowledge the use of a Zemax licence for optical design and analysis in this research.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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