The axial resolution of confocal microscopy is not only dependent on optical characteristics but also on the utilized peak extraction algorithms. In previous evaluations of peak extraction algorithms, sample surface height is generally assumed to be zero, and only sampling-noise-induced peak extraction uncertainty was analyzed. Here we propose a sample surface-height-dependent (SHD) evaluation model that takes the combined considerations of sample surface height and noise for comparisons of algorithms' performances. Monte Carlo simulations were first conducted on the centroid algorithm and several nonlinear fitting algorithms such as the parabola fitting algorithm, Gaussian fitting algorithm, and sinc2 fitting algorithm. Subsequently, the evaluation indicators, including mean peak extraction error and mean uncertainty were suggested for the algorithms' performance ranking. Finally, experimental verifications of the SHD model were carried out using a fiber-based chromatic confocal system. From our simulations and experiments, we demonstrate that sample surface height is a critical influencing factor in peak extraction computation in terms of both the accuracy and standard deviations. Compared to the conventional standard uncertainty evaluation model, our SHD model can provide a more comprehensive characterization of peak extraction algorithms' performance and offer a more flexible and consistent reference for algorithm selection.

Influence of sample surface height for evaluation of peak extraction algorithms in confocal microscopy

Focused and controllable optical delivery beyond the optical diffusion limit in biological tissue has been desired for long yet considered challenging. Digital optical phase conjugation (DOPC) has been proven promising to tackle this challenge. Its broad applications, however, have been hindered by the system’s complexity and rigorous requirements, such as the optical beam quality, the pixel match between the wavefront sensor and wavefront modulator, as well as the flatness of the modulator’s active region. In this paper, we present a plain yet reliable DOPC setup with an embedded four-phase, non-iterative approach that can rapidly compensate for the wavefront modulator’s surface curvature, together with a non-phase-shifting in-line holography method for optical phase conjugation in the absence of an electro-optic modulator (EOM). In experiment, with the proposed setup the peak-to-background ratio (PBR) of optical focusing through a standard ground glass in experiment can be improved from 460 up to 23,000, while the full width at half maximum (FWHM) of the focal spot can be reduced from 50 down to 10 μm. The focusing efficiency, as measured by the value of PBR, reaches nearly 56.5% of the theoretical value. Such a plain yet efficient implementation, if further engineered, may potentially boost DOPC suitable for broader applications.

/pdf/implementation-of-digital-optical-phase-conjugation-with-22h7l8y1pn.pdf

Implementation of digital optical phase conjugation with embedded calibration and phase rectification.

Accurate and reliable peak extraction of axial response signals plays a critical role in confocal microscopy. For axial response signal processing, nonlinear fitting algorithms, such as parabolic, Gaussian or sinc2 fitting may cause significant systematic peak extraction errors. Also, existing error compensation methods require a priori knowledge of the full-width-at-half-maximum of the axial response signal, which can be difficult to obtain in practice. In this paper, we propose a generalised error compensation method for peak extraction from axial response signals. This full-width-at-half-maximum-independent method is based on a corrected parabolic fitting algorithm. With the corrected parabolic fitting algorithm, the systematic error of a parabolic fitting is characterised using a differential equation, following which, the error is estimated and compensated by solving this equation with a first-order approximation. We demonstrate, by Monte Carlo simulations and experiments with various axial response signals with symmetrical and asymmetrical forms, that the corrected parabolic fitting algorithm has significant improvements over existing algorithms in terms of peak extraction accuracy and precision.

Corrected parabolic fitting for height extraction in confocal microscopy

High focusing accuracy in microscopes could improve the imaging quality to reduce the error rate in DNA sequencing. We propose a new feedback method to improve the focusing condition to a very high accuracy. A reference laser reflected by the sample is detected by two or more sensors around the confocal point. After acquiring the signals from the out-of-focus positions, online data processing is implemented to provide feedbacks for real-time focus-plane locking on the sample surface. This method provides an accuracy better than 1/10 of the objective depth-of-focus. To balance optical aberrations, a specific optical feedback system should be designed, with athermal design considerations to adapt DNA sequencing work to temperature fluctuations.

Improvement in focusing accuracy of DNA sequencing microscope with multi-position laser differential confocal autofocus method

To improve the positioning capabilities of a chromatic confocal displacement measurement system, we introduce a super-resolving pupil filtering element (referred to as spatial-bandpass-filter), an X-shaped fiber-coupler, and a modified peak-extraction algorithm. The spatial-bandpass-filer decreases the spherical aberration of conventional refractive lenses and transmission loss, without changing the dispersion range. The new optical design minimizes the effect of light-source-variation as well as reflectance-variation of the sample surface against the wavelength by adding a reference arm with an X-shaped fiber-coupler and normalization algorithm. This enables rapid re-purposing to obtain data for crosstalk, reference and measurement signals. A prototype setup was built and the experimental results show that the new chromatic dispersion system can reach a position stability of ± 0.36 μm using a commercial cost-effective white-light source. It reaches an axial displacement resolution of up to 1 μm and a peak-fit error below ± 0.2% for a range of 1.05 mm.

Improved chromatic confocal displacement-sensor based on a spatial-bandpass-filter and an X-shaped fiber-coupler.

A laser reflection-confocal focal-length measurement (LRCFM) is proposed for the high-accuracy measurement of lens focal length. LRCFM uses the peak points of confocal response curves to precisely identify the lens focus and vertex of the lens last surface. LRCFM then accurately measures the distance between the two positions to determine the lens focal length. LRCFM uses conic fitting, which significantly enhances measurement accuracy by inhibiting the influence of environmental disturbance and system noise on the measurement results. The experimental results indicate that LRCFM has a relative expanded uncertainty of less than 0.0015%. Compared with existing measurement methods, LRCFM has high accuracy and a concise structure. Thus, LRCFM is a feasible method for high-accuracy focal-length measurements.

Measuring the lens focal length by laser reflection-confocal technology

A new laser differential confocal ultra-long focal length measurement (LDCFM) method is proposed with the capability to self-calibrate the reference lens (RL) focal length and the axial space between the test lens and RL. Using the property that the focus of laser differential confocal ultra-long focal length measurement system (LDCFS) precisely corresponds to the null point of the differential confocal axial intensity curve, the proposed LDCFM measures the RL focal length fR′ by precisely identifying the positions of the focus and last surface of RL, measures the axial space d0 between RL and test ultra-long focal length lens (UFL) by identifying the last surface of RL and the vertex of UFL last surface, and measures the variation l in focus position of LDCFS with and without test UFL, and then calculates the UFL focal length fT′ by the above measured fR′, d0 and l. In addition, a LDCFS based on the proposed method is developed for a large aperture lens. The experimental results indicate that the relative uncertainty is less than 0.01% for the test UFL, which has an aperture of 610 mm and focal length of 31,000 mm. LDCFM provides a novel approach for the high-precision focal-length measurement of large-aperture UFL.

Large-aperture laser differential confocal ultra-long focal length measurement and its system.

Method for measuring focal length of reflection type confocal lens

Autocollimating type confocal method for measuring focal length of lens

The invention belongs to the technical field of optical precision measurement, and relates to a multi-reflection laser differential confocal long focal length measuring method and a multi-reflection laser differential confocal long focal length measuring device. According to the method, a parallel optical flat and a reflector are introduced behind a measured mirror to reflect a focused beam multiple times, the convergence points for different reflection times after multiple times of back-turning are focused at high precision based on the fact that the zero-crossing point of a laser differential confocal light intensity response curve precisely correspond to the convergence point, and then, the position information of the reflector is measured precisely by a length measuring interferometer, thus realizing high-precision long focal length measurement. By adopting the method integrating a differential confocal focusing principle and a multi-reflection turn-back principle, the measuring light path is compressed heavily, the measuring distance is shortened greatly, the instrument structure is simplified, and the resistance to environmental interference is improved. The method and the device of the invention can be used for high-precision measurement of the focus length of a long-focal-length lens or optical system.

Multi-reflection laser differential confocal long focal length measuring method and multi-reflection laser differential confocal long focal length measuring device

Zhigang Li

Papers

Measuring the lens focal length by laser reflection-confocal technology

Large-aperture laser differential confocal ultra-long focal length measurement and its system.

Method for measuring focal length of reflection type confocal lens

Autocollimating type confocal method for measuring focal length of lens

Multi-reflection laser differential confocal long focal length measuring method and multi-reflection laser differential confocal long focal length measuring device