Chromatic Focal Shift Research Articles

Confocal corrected attenuation coefficient imaging in phantoms and in vivo using chromatic focal shift calibration.

Optical coherence tomography (OCT) is conventionally used for structural imaging of tissue. Calibrating the intensity values of OCT images can give information on the tissue's inherent optical properties, such as the attenuation coefficient, which can provide an additional parameter to quantify possible pathological changes. To obtain calibrated intensity values, the focus position and Rayleigh length of the incident beam need to be known. We explore the feasibility of extracting the focus position from an OCT scan acquired with a single focus setting using the chromatic aberration of the system. The chromatic focal shift of an OCT system is exploited to achieve different focus positions for sub-spectrum reconstructed OCT images. The ratios of these images are used to estimate the focus position. Reconstruction of a high-resolution B-scan from coherent addition of sub-spectrum confocal function corrected B-scans and subsequent high-resolution OCT attenuation coefficient imaging is demonstrated. Furthermore, we introduce a method to experimentally determine the chromatic focal shifts of an OCT system in phantoms and an in vivo human retina. These shifts are compared to the theoretically expected shifts calculated with ray tracing.

Tunable doublets: piezoelectric glass membrane lenses with an achromatic and spherical aberration control.

We present two versions of tunable achromatic doublets based on each two piezoelectrically actuated glass membranes that create the surface of fluid volumes with different dispersions: a straightforward back-to-back and a more intricate stack of the fluid volumes. In both cases, we can control the chromatic focal shift and focal power independently by a suitable combination of actuation voltages on both active membranes. The doublets have a large aperture of 12 mm at an outer diameter of the actuator of 18 mm, an overall thickness of 3 mm and a short response time of around 0.5 ms and, in addition, provide spherical aberration correction. The two designs have an achromatic focal power range of ±2.2 m-1 and ±3.2 m-1 or, for the purpose of actively correcting chromatic errors, a chromatic focal shift at vanishing combined focal power of up to ±0.08 m-1 and ±0.12 m-1.

VIS-NIR superachromatic triplet design with five-color correction for a broadband interferometer.

In general, k lenses with different materials can achieve at most (k+1) color correction (k≥2). A superachromat containing three lenses is designed to achieve five-color correction in the 600-1600 nm waveband, where the maximum chromatic focal shift is controlled within 1/100,000 of the focal length, achieving an almost unprecedented result. Conditions for lens power combination of three thin lenses in contact are first derived based on the Buchdahl dispersion equation; then a metric is introduced to verify the five-color correction, and a correction method is proposed to improve the refractive index fitting accuracy of the Buchdahl model from ∼10-3 to ∼10-7. By traversing 197 ecofriendly glass materials in the CDGM glass library iteratively, 113 initial structures are obtained in only 61.75 s, from which the structure with the minimum chromatic focal shift is selected to be optimized with Opticstudio. By setting up required operands, the final structure being within the diffraction limit in a field of view of ±0.05∘ is obtained within only 6 s, where the maximum longitudinal chromatic aberration is close to the maximum chromatic focal shift. We provide a complete theoretical basis and important guidance for designing broadband superachromats with (k+2) color correction using only k lenses and the smallest chromatic focal shift, and based on the theories, we have developed a broadband interferometer.

Hybrid ray-tracing/Fourier optics method to analyze multilayer diffractive optical elements.

The performance (paraxial phase delay) of conventional diffractive optical elements is generally analyzed using the analytical scalar theory of diffraction, based on thin-element approximation (TEA). However, the high thickness of multilayer diffractive optical elements (MLDOEs) means that TEA yields inaccurate results. To address this, we tested a method based on ray-tracing simulations in mid-wave and long-wave infrared wave bands and for multiple f-numbers, together with the effect of MLDOE phase delay on a collimated on-axis beam with an angular spectrum method. Thus, we accurately generate optical figures of merit (point spread function along the optical axis, Strehl ratio at the "best" focal plane, and chromatic focal shift) and, by using a finite-difference time-domain method as a reference solution, demonstrate it as a valuable tool to describe and quantify the longitudinal chromatic aberration of MLDOEs.

Enabling consumer-grade 3D-printed optical instruments – a case study on design and fabrication of a spectrometer system using low-cost 3D printing technologies

3D printing of optical components can broaden access to optical fabrication. However, consumer options for 3D printing have been limited due to the form and roughness requirements for optics. Previous efforts have established a protocol for the fabrication of singlet lenses using a stereolithographic printer and simple post-processing techniques. Here we further elevate this research by building a consumer-grade 3D printed spectrometer utilizing achromatic doublet printed lenses. These lenses are fabricated using stereolithographic printers with a filled cavity and reduce chromatic focal shift by a factor of 6 over singlet lenses. The proof-of-concept spectrometer system incorporates a pinhole, two doublet lenses, and a dispersing prism. Opto-mechanics for the system were fabricated using an FDM 3D printer. Results from the fabricated system closely matched results obtained with a commercially available spectrometer device.

Fiber-optic large-depth 3D chromatic confocal endomicroscopy.

Current endoscopy techniques have difficulties to provide both high resolution and large imaging depth, which significantly hinders the early diagnosis of gastric cancer. Here, we developed a label-free, large-depth, three-dimensional (3D) chromatic reflectance confocal endomicroscopy. In order to solve the problem of insufficient imaging depth of traditional chromatic confocal microscopy, a customized miniature objective lens both with large chromatic focal shift and correction for spherical aberration was used to focus light of different wavelengths at different depths of the sample simultaneously, and a fiber bundle containing 50000 single-mode cores was used to collect the confocal reflectance signal. To acquire detailed information along the axial direction at a faster speed, a high-speed multi-pixel spectrometer was used to realize simultaneous detection of multi-depth signals. Specifically, we have built up a label-free fiber-optic 3D chromatic reflectance confocal endomicroscopy, with 2.3 µm lateral resolution, imaging depth of 570 µm in 3D phantom and 220 µm in tissue, and 1.5 Hz 3D volumetric frame rate. We have demonstrated that the fiber-optic 3D chromatic confocal endomicroscopy can be used to image human gastric tissues ex vivo, and provide important morphological information for diagnosis without labeling. These results show the great potential of the fiber-optic 3D chromatic confocal endomicroscopy for gastric cancer diagnosis.

Simultaneous Achromatic and Varifocal Imaging with Quartic Metasurfaces in the Visible

Two key metrics for imaging systems are their magnification and optical bandwidth. While high-quality imaging systems today achieve bandwidths spanning the whole visible spectrum and large changes in magnification via optical zoom, these often entail lens assemblies with bulky elements unfit for size-constrained applications. Metalenses present a methodology for miniaturization but their strong chromatic aberrations and the lack of a varifocal achromatic element limit their utility. While exemplary broadband achromatic metalenses are realizable via dispersion engineering, in practice, these designs are limited to small physical apertures as large area lenses would require phase compensating scatterers with aspect ratios infeasible for fabrication. Many applications, however, necessitate larger areas to collect more photons for better signal-to-noise ratio and furthermore must also operate with unpolarized light. In this paper, we simultaneously achieve achromatic operation at visible wavelengths and varifocal control using a polarization-insensitive, hybrid optical-digital system with area unconstrained by dispersion-engineered scatterers. We derive phase equations for a pair of conjugate metasurfaces that generate a focused accelerating beam for chromatic focal shift control and a wide tunable focal length range of 4.8 mm (a 667-diopter change). Utilizing this conjugate pair, we realize a near spectrally invariant point spread function across the visible regime. We then combine the metasurfaces with a post-capture deconvolution algorithm to image full-color patterns under incoherent white light, demonstrating an achromatic 5x zoom range. Simultaneously achromatic and varifocal metalenses could have applications in various fields including augmented reality, implantable microscopes, and machine vision sensors.

Long-focus low-cost lens deigned for biomedical hyperspectral camera

In this work a design of 250 mm F/20 lens for hyperspectral imaging of biomedical micro objects is presented. The designed lens consists of only standard optical elements and does not contain any newly developed component. Its low aperture and small field of view causes that image quality is limited only by diffraction and two optical aberrations – field curvature and chromatic focal shift. That is why an achromatic doublet is utilized as a basic lens component. Its residual field curvature is corrected by a Smith lens – a single plane-concave lens located near the image plane. The components are selected from commercially available ones. A distance between components was the only optimized parameter. Such layout makes the lens cheap and easy to manufacture.

Comparison study of a multispectral zoom lens using standard and novel optical materials.

We demonstrate two broadband multispectral infrared (3.5-11.5 μm), zoom (3×) systems with focal lengths adjustable from 50 mm to 150 mm. Both systems are successful in meeting the modulation transfer function (MTF) requirement of 20 lp/mm. The difference between the two designs is that one employs novel infrared-transparent glasses that permit the designer to achieve an improved system performance with dramatically fewer lens elements. The impact of these materials on the design performance is discussed in terms of MTF and chromatic focal shift as a function of temperature, and we conclude with a brief description of these new glasses and their optical functionality.

Extending the depth of focus of fiber-optic optical coherence tomography using a chromatic dual-focus design.

We report a dual-focus fiber-optic probe designed to extend depth of focus (DOF) in high-resolution endoscopic optical coherence tomography. We exploited the broad spectral bandwidth of a supercontinuum source and, in the fiber probe, the foci of the 750-1000nm and 1100-1450nm inputs were axially chromatically shifted. The interference signals from the two spectral bands were measured with a Si camera-based spectrometer and an InGaAs camera-based spectrometer, respectively. We verified the feasibility of the design using a phantom composed of microparticles and swine small intestine tissue ex vivo. The results showed that a transverse resolution below 5μm over 300μm could be maintained, and that the extended DOF was 2times larger than that of the single focus probe via the use of dual spectral band inputs and a chromatic focal shift.

High-speed, ultrahigh-resolution distal scanning OCT endoscopy at 800 nm for in vivo imaging of colon tumorigenesis on murine models.

We present the first, most compact, ultrahigh-resolution, high-speed, distal scanning optical coherence tomography (OCT) endoscope operating at 800 nm. Achieving high speed imaging while maintaining an ultrahigh axial resolution is one of the most significant challenges with endoscopic OCT at 800 nm. Maintaining an ultrahigh axial resolution requires preservation of the broad spectral bandwidth of the light source throughout the OCT system. To overcome this critical limitation we implemented a distal scanning endoscope with diffractive optics to minimize loss in spectral throughput. In this paper, we employed a customized miniature 900 µm diameter DC micromotor fitted with a micro reflector to scan the imaging beam. We integrated a customized diffractive microlens into the imaging optics to reduce chromatic focal shift over the broad spectral bandwidth of the Ti:Sapphire laser of an approximately 150 nm 3dB bandwidth, affording a measured axial resolution of 2.4 µm (in air). The imaging capability of this high-speed, ultrahigh-resolution distal scanning endoscope was validated by performing 3D volumetric imaging of mouse colon in vivo at 50 frames-per-second (limited only by the A-scan rate of linear CCD array in the spectral-domain OCT system and sampling requirements). The results demonstrated that fine microstructures of colon could be clearly visualized, including the boundary between the absorptive cell layer and colonic mucosa as well the crypt patterns. Furthermore, this endoscope was employed to visualize morphological changes in an enterotoxigenic Bacteriodes fragilis (ETBF) induced colon tumor model. We present the results of our feasibility studies and suggest the potential of this system for visualizing time dependent morphological changes associated with tumorigenesis on murine models in vivo.

Comparative analysis of the Fresnel lens and the kinoform lens

Based on a unified approach in the ray approximation, the focusing properties of Fresnel lenses and kinoform lenses are considered and compared. Particular attention is paid to the energy efficiency, chromatic focal shift and resolving power of these elements. It is shown that the Fresnel lens with same-depth segments is an analogue of the harmonic kinoform lens operating in high diffraction orders. A mechanism of the formation of the diffraction pattern in the focal plane of a Fresnel lens with equidistant annular segments is analyzed. It is shown to differ from the corresponding diffraction pattern formed by a conventional refractive lens by a smaller amount of energy coming to the main maximum and a significant proportion of energy transferred to the side maxima. The target audience of this article is students and graduate students, as well as specialists in the fields of science and technology where optical methods and instruments play an ever increasing role.

Method to design apochromat and superachromat objectives

We present a simple method to design apochromat and superachromat objectives. The chromatic focal shift is used to determine glass combinations that yield three and four crossings in the chromatic focal shift curve. The method can be extended to design superachromats with more than four crossings.

Chromatic aberrations correction for imaging spectrometer based on acousto-optic tunable filter with two transducers.

The acousto-optic tunable filter (AOTF) with wide wavelength range and high spectral resolution has long crystal and two transducers. A longer crystal length leads to a bigger chromatic focal shift and the double-transducer arrangement induces angular mutation in diffracted beam, which increase difficulty in longitudinal and lateral chromatic aberration correction respectively. In this study, the two chromatic aberrations are analyzed quantitatively based on an AOTF optical model and a novel catadioptric dual-path configuration is proposed to correct both the chromatic aberrations. The test results exhibit effectiveness of the optical configuration for this type of AOTF-based imaging spectrometer.

Design, tolerance analysis, fabrication, and testing of a 6-in. dual-wavelength transmission sphere for a Fizeau interferometer

This paper presents the validation of the design of a 6-in. f/2.2 dual-wavelength transmission sphere (TS) based on the Fizeau interferometer. The TS was verified at a wavelength of 632.8 nm and is compatible for measuring the transmitted wavefront error of an i-line lithography lens. The achromatic design is imperative for a dual wavelength TS and requires more lenses for correcting the chromatic focal shift. Because the overall weight of the TS should be controlled within the load range of the piezoelectric transducers of the interferometer, the fabrication and mounting of lenses with high aspect ratios are challengeable. The mounting of the reference surface based on three-point mounting was successful for the residual reference wavefront error under peak-to-valley (PV) λ/10. Furthermore, the reference wavefront is typically restricted within PV 5λ to avoid distorted interference fringes. Therefore, we built a double-pass interferometer model for tolerance analysis, and the error budget facilitated decision-making regarding the suitable specifications of lens manufacturing and assembly for cost efficiency. The test results demonstrated that the deformation of the reference wavefront and the residual reference wavefront error met the critical specification at 632.8 nm and that the achromatic TS is compatible for measuring i-line lithography lenses.

Measuring chromatic aberrations in imaging systems using plasmonic nanoparticles.

We demonstrate a method to measure chromatic aberrations of microscope objectives with metallic nanoparticles using white light. Extinction spectra are recorded while scanning a single nanoparticle through a lens's focal plane. We show a direct correlation between the focal wavelength and the longitudinal chromatic focal shift through our analysis of the variations between the scanned extinction spectra at each scan position and the peak extinction over the entire scan. The method has been tested on achromat and apochromat objectives using aluminum disks varying in size from 260-520 nm. Our method is straightforward, robust, low cost, and broadband with a sensitivity suitable for assessing longitudinal chromatic aberrations in high-numerical-aperture apochromatic corrected lenses.

F/1.6 diffraction-limited air-spaced Cooke triplet photographic lens designs for MWIR and LWIR imaging applications: geometrical optics performance comparison between Ge–ZnSe–Ge and Si–Ge–Si triplet designs using Zemax

In this study Ge–ZnSe–Ge (spectral range 8–14μm) and Si–Ge–Si (spectral range 3–11μm) air-spaced photographic objective triplet lens designs are discussed. The two designs have focal length of 90mm, f/1.6 and full field-of-view (FOV) of±4.5°. Geometrical optics calculations obtained with Zemax® for each lens design are provided for the modulation transfer function (MTF), point spread function (PSF), encircled energy, transverse ray fan plots, root-mean-square wave front error (RMS WFE), chromatic focal shift, field curvature, distortion, and RMS WFE versus wavelength. Furthermore, the MTF at 50% contrast modulation for both designs is evaluated over the temperature range 20–40°C. The results indicate that the Ge–ZnSe–Ge triplet design is more susceptible to temperature variations, which lead to loss in image quality with the rise in ambient temperature

Design of high-performance adaptive objective lens with large optical depth scanning range for ultrabroad near infrared microscopic imaging.

We report on the theory and design of adaptive objective lens for ultra broadband near infrared light imaging with large dynamic optical depth scanning range by using an embedded tunable lens, which can find wide applications in deep tissue biomedical imaging systems, such as confocal microscope, optical coherence tomography (OCT), two-photon microscopy, etc., both in vivo and ex vivo. This design is based on, but not limited to, a home-made prototype of liquid-filled membrane lens with a clear aperture of 8mm and the thickness of 2.55mm ~3.18mm. It is beneficial to have an adaptive objective lens which allows an extended depth scanning range larger than the focal length zoom range, since this will keep the magnification of the whole system, numerical aperture (NA), field of view (FOV), and resolution more consistent. To achieve this goal, a systematic theory is presented, for the first time to our acknowledgment, by inserting the varifocal lens in between a front and a back solid lens group. The designed objective has a compact size (10mm-diameter and 15mm-length), ultrabroad working bandwidth (760nm - 920nm), a large depth scanning range (7.36mm in air) - 1.533 times of focal length zoom range (4.8mm in air), and a FOV around 1mm × 1mm. Diffraction-limited performance can be achieved within this ultrabroad bandwidth through all the scanning depth (the resolution is 2.22 μm - 2.81 μm, calculated at the wavelength of 800nm with the NA of 0.214 - 0.171). The chromatic focal shift value is within the depth of focus (field). The chromatic difference in distortion is nearly zero and the maximum distortion is less than 0.05%.

Large aperture adaptive doublet polymer lens for imaging applications.

We report a full design process-finite element modeling, fabrication, and characterization-of adaptive doublet polymer lenses. A first-order model was developed and used to design fluidic doublets, analogous to their glass counterparts. Two constant-volume fluidic chambers were enclosed by three flexible membranes, resulting in a variable focal length doublet with a clear aperture of 19.0 mm. Chromatic focal shift was then used to compare numerical modeling to experimentally measured results over a positive focal length range of 55-200 mm (f/2.89 to f/10.5).

Achromatic correction of diffractive dispersion in white light SLM imaging.

In contemporary optics, the spatial light modulator (SLM) is effectively used as a flexible optoelectronic device playing the key role in a number of experiments of science and technology. Its operation is optimal when using almost monochromatic light but an extremely strong diffractive dispersion occurs when white light is applied. In this paper, the design concepts are proposed resulting in optimization and implementation of a refractive corrector cooperating with the SLM. The corrector maintains the operation of the SLM unchanged for the central wavelength of light and ensures an achromatic dispersion compensation throughout the visible region in applications based on a lens-pattern formation. A significant improvement of the imaging performance of the achromatic SLM was proved by the computer simulation and measurement of the chromatic focal shift and the image contrast of the resolution target.