Methods and systems for dynamic z-scanning, and single-lens addition to microscopy

Abstract

Systems capable of in situ position detection, thickness and refractive index measurement, and / or focus control, are provided. The systems may include a first laser emitting device, a first lens, a first beam splitter and a second lens respectively forming an optical path. The second lens, the first beam splitter, a third lens, and an image detection and processing module (that includes a sensor, such as a photodiode) may form an optical return path. The second lens may be configured to continuously oscillate, as a function of time, a focal position of a laser from the first laser emitting device. The image detection and processing module may be configured to receive a reflected beam, send information related to the received beam to processing units(s), which may be configured to receive the information and determine one or more surface positions based on a temporal response of the information.

Description

[0001]Princeton - 95376 METHODS AND SYSTEMS FOR DYNAMIC Z-SCANNING, AND SINGLE-LENS ADDITION TO MICROSCOPY CROSS-REFERENCE TO RELATED APPLICATIONS The present application claims priority to 63 / 529,525, filed July 28, 2023, the contents of which are incorporated by reference herein in its entirety. TECHNICAL FIELD The present disclosure is drawn to optical techniques for, e.g., ultrafast position detection, thin film thickness detection and / or refractive index measurement. BACKGROUND Measuring thin film thickness and refractive index is crucial for research and industrial applications. Optical techniques are among the most developed thickness measurement methods since they allow non-contact, nondestructive measurements, particularly important for fragile samples such as biological tissues and flexible thin films. Depending on inspection conditions and sample properties, the thickness of a thin film can be measured using reflectometry, ellipsometry, interferometry, or confocal microscopy. While reflectometry and ellipsometry measure the intensity or polarization of the reflected light, interferometry and confocal microscopy commonly involve axial scanning motions of optical elements to create optical path differences. For example, in low coherence Michelson interferometry, the mirror in the reference arm is translated to obtain peak interference contrast between the reference beam and the reflected beam from multiple surfaces. In confocal microscopy, the focusing lens or the sample mounting stage scans in z to obtain the peak reflected confocal signal from multiple surfaces. In both cases, the translated distance of the optical elements between the top and bottom surface of the thin film is used to calculate its thickness and refractive index. No matter which optical element is movable in interferometry or confocal microscopy, the axial movement is usually a mechanical motion driven by motorized stages, which scan stepwise during measurement processes. However, this mechanical stepwise motion slows down the thickness measurement processes due to accelerations / deceleration in each movement step, limiting the temporal resolution of the measurement. The bottleneck of axial motion is particularly significant in confocal microscopy requiring 3D volumetric acquisition, where the x-y raster scanning by galvo mirrors, rotating disks, or micro-lens arrays can go up to 500 Hz, while the z movement by stages or objective lenses is orders of magnitude slower. Princeton - 95376 Additionally, traditional auto-focusing techniques for laser processing consist of two independent modules: 'detection and movement', i.e., first, in-situ and non-destructive detection of the surface location; second, z-axis movement by physically moving either the sample or the focusing lens. Almost all optical metrology with automatic focus alignment still requires the mechanical motion of a z-stage attached to the sample or the focusing lens as the second 'movement' module in its feedback loop, which limits the response rate and the overall speed of focus control. Even with the advance of the fast mechanical stages and scanning galvo- mirrors, adjusting z position can be up to three orders of magnitude slower than the lateral speed of adjusting x and y due to mechanical acceleration / deceleration. The process of surface detection and the further re-alignment between the focus and the measured surface need to be accelerated. BRIEF SUMMARY In various aspects, a system for in situ position detection, thickness and refractive index measurement, and focus control may be provided. The system may include a first laser emitting device, a first lens, a first beam splitter and a second lens may form an optical path (e.g., a probing beam transmit path). The first lens may be configured to continuously oscillate, as a function of time, a focal position of a laser from the first laser emitting device. The first lens may be a liquid tunable acoustic gradient index lens (TAG lens). The second lens, the first beam splitter, a third lens, and an image detection and processing module may form an optical return path (e.g., the probing beam return path). The image detection and processing module may include a photodiode. The image detection and processing module may be configured to receive a reflected beam. The image detection and processing module may include an oscilloscope coupled to the photodiode. The image detection and processing module may be configured to send information related to the reflected beam to one or more processing unit(s), such as a remote processing unit. The one or more processing unit(s) may be, collectively, configured to receive the information and determine one or more surface positions based on a temporal response of the information. The one or more remote processing unit(s) may include processing unit(s) within a computer operably coupled to the oscilloscope. The computer may be configured to calculate the position, thickness or refractive index of the target object based on the information related to the received reflected beam. The system may include a filter configured to remove out-of-focus light, the filter disposed between the third lens and the photodiode. Princeton - 95376 The system may include a target object forming an end of the optical path and a beginning of the optical return path. The system may include a TAG controller. When the first lens is a TAG lens, the TAG lens may be coupled to the TAG controller. The TAG controller may be configured to (i) modify a frequency of the TAG lens, and (ii) control an output of a laser emitting device. The system may include a second laser emitting device and a second beam splitter. The second laser emitting device, the second beam splitter, the first lens, the first beam splitter, and second lens respectively form an optical path (e.g., a fabrication beam transmit path). The second laser emitting device may be coupled to a controller (such as the TAG controller). In various aspects, a method for position detecting and focus control may be provided. The method may include sending a first laser beam through a first lens (such as a TAG lens), a first beam splitter, a second lens, and towards a target object. The method may include directing a reflection of the first laser beam from the target object through the second lens and towards the first beam splitter. The method may include directing the reflection from the target object from the first beam splitter through a third lens towards an image detection and processing module. The method may include collecting laser beam signal data using the image detection and processing module. The method may include using the signal data to calculate the position, thickness or refractive index of the target object. The method may include sending a second laser beam from a laser source through a second beam splitter, the first lens, the first beam splitter, the second lens and towards the target object. The method may include operably coupling a TAG controller to the TAG lens and the laser source of the second laser beam. The method may include using the TAG controller to adjust a frequency of the TAG lens according to the signal data. The method may include using the TAG controller to control the second laser beam according to an oscillation phase of the TAG lens. The method may include physically marking a surface using the second laser beam. In various aspects, a system may be provided. The system may include a dynamic z- scanning lens configured to be operably coupled to a microscope in a laser transmit path of a laser emitting source of the microscope. A controller may be operably coupled to the z- scanning lens, the controller configured to modify a frequency of the dynamic z-scanning lens. a signal detection module may be configured to be operably coupled to the microscope. The signal detection module may include a photodiode detector configured to receive light from the laser emitting source after passing through the dynamic z-scanning lens and reflecting off at least one surface. The controller may include at least one processing unit. The system may include a non-transitory computer-readable storage device containing instructions that, when Princeton - 95376 executed by the at least one processing unit, causes the at least one processing unit to, collectively, perform various steps. Such steps may include, e.g., modifying the frequency of the dynamic z-scanning lens, and determining one or more surface positions, thickness, and refractive index based on a temporal response of the light after reflecting off the at least one surface. BRIEF DESCRIPTION OF FIGURES Figure 1A is a schematic of a system. Figure 1B is a schematic illustration of a TAG lens oscillation controlling the axial focal length (z) of a laser beam over time. Figure 2 is a flowchart of a method. Figure 3A is a plot of one period of focus scanning zf(t) and the surface position ^^Sat multiple locations (A-G) within the scanning range. Figure 3B is a plot of acquired photodiode (PD) signal for locations A-G. The recognized double peaks correspond to the condition of zf(t) = ^^S, and the peak-to-peak time interval is denoted by Δ ^^. Figure 4 is a plot of the measured cos(πΔt / T) versus the real surface position ^^S for a system using a 40x objective lens; a linear fit defines the calibrated surface position ^^ௌᇱ, with the fitted intercept as z0and the slope as ztag. Figure 5 are plots showing the normalized signal of the photodiode at location z1, z2, and z3for the three calibration experiments with different driving voltages. Figure 6 is a box and whisker chart of the errors δz = ^^ௌᇱ= ^^Sfor calibration experiments with an objective lens of 40x and Vtag = 15 V (A1-A6). Figure 7 is a graph showing calibrated surface position ^^Swith the fitted intercept (z0) and slope (ztag) a 4x objective lens and Vtag= 15 V. Figure 8 is a plot showing a measured profile of the step surface with three repeated experiments (i and ii with calibration B1, iii with calibration B2). Figures 9A and 9B are plots showing normalized photodiode signals for experiment i at the low surface (x = 0 mm) (9A) and the high surface (x = 10 mm) (9B). The time interval Δt is measured as 0.64T and 0.4T , respectively. Figure 10 shows examples of various focusing strategies for laser marking on a step surface with only one later translation in x and no motion in z; the subplots show the same number (=16) of pulses; the step surface profile zS(x) is in a dashed line with its low and high Princeton - 95376 surface located at zS1 and zS2, and the solid black line plots the laser focal position as a function of x. Deposited pulses are represented by markers, with defocused pulses in circles, focused pulses at zS1 and zS2 in triangles and diamonds, respectively. Figure 11 are schematics and images showing laser marking on a step surface with various focusing strategies. The scale bars are 100 µm. Figure 12 are zoom-in views of the selective marking lines A-D show the percentages of focused pulses over all the deposited pulses on Surface 1 and 2; focused and defocused pulses are represented by the markers as indicated. The scale bars are 30 μm. Figures 13A, 13B, and 13C are plots showing real-time detected surface position against time at the end of each measurement in videos V1 and V2 – V1 with z speed of 0.02 mm / s and z acceleration of ± 0.002 mm / s2(13A) or ± 0.1 mm / s2(13B); or detection of a step surface in V2 with an x speed of 0.1 mm / s (13C). Figures 14A and 14B show plots of surface position (14A) and matching phase (14B) during the auto-focusing laser marking of a two-step surface in a video V3. The three surfaces are labeled by A, B, and C. Figure 15 shows a 3D microscopy of the two-step surface (from Figure 14) showing the laser marking line on all three surfaces, indicating auto-focusing without any z stage motion. The total marking length shown in the 3D microscope image is 14416 μm. Figure 16 is a schematic of a system. Figure 17 is a schematic for measuring the thickness of a thin film placed within the axial scanning range of the TAG lens, showing the bottom ( ^^1) and the top surface ( ^^2). Figure 18A is a plot of one period of focus scanning ^^^^( ^^) and positions of the top and bottom surface. Figure 18B is a plot of acquired normalized photodiode signal; the quadruple peaks correspond to the conditions of ^^^^( ^^) = ^^1and ^^^^( ^^) = ^^2. The peak-to-peak time intervals are denoted by Δ ^^1and Δ ^^2, respectively. Figures 19A and 19B are plots showing characterization of the constructed position sensor for detecting a single surface located at ^^Sfor two calibration experiments, i (19A) and ii (19B); the primary y-axis plots cos( ^^Δ ^^ / ^^) in and a linear fit based on Eq. (4). The secondary y-axis displays the error ^^ ^^ between the fitted and real values of ^^S. Figures 19C and 19D show plots of the PD signals for three different ^^ locations at ^^1, ^^2, and ^^3 for calibration i (19C) and ii (19D), showing double peaks separated with different time intervals. Princeton - 95376 Figure 20 is a schematic illustrating a sample stage moves down by 0.5 ^^m each step for No.1 to 5. Figures 21A and 21B are plots of acquired time intervals Δ ^^ / ^^ (21A) and surface positions (21B) of the bottom surface and the top surface for PI film-A. Figures 21C and 21D are plots of acquired time intervals Δ ^^ / ^^ (21C) and surface positions (21D) of the bottom surface and the top surface for PI film-B. Figures 21E and 21F are plots showing calculated thickness ^^ for PI film-A (21E) and PI film-B (21F). Figures 22A and 22B are plots showing characterization of the constructed optical setup with a 10x objective lens; the primary y-axis plots cos( ^^Δ ^^ / ^^) and a linear fit based on Eq.1; the secondary y-axis displays the error ^^ ^^ between the fitted and real values of ^^S. Figure 22C is a plot showing measured positions for ^^1 and z2 for the thin glass; the sample stage moves up by 0.05 mm for each step for No.1 to 5, as indicated by values of ^^ ^^ (from -0.2 mm to 0 mm). Figure 22D is a plot showing of five example signals showing identified peaks are taken when ^^^^is positioned between -0.3 mm to 0.1 mm. Triangular markers denote the recognized pairs of double peaks, whereas circular markers represent the merging peaks. Figure 22E is a plot of calculated thickness ^^ and refractive index ^^ of the thin glass and the sapphire plates. DETAILED DESCRIPTION One way to accelerate the focus alignment after position detection is to incorporate fast axial varifocal optics such as deformable mirror, tunable liquid or liquid crystal lens, manipulating the focal position and bypassing delays in acceleration / deceleration from any mechanical motion. Leveraging the ultrafast beam shaping speed of varifocal lenses, one can transform the 'detection and movement' strategy, and utilize a single lens approach to integrate both 'detection' and 'movement' at the same time. To integrate the two modules as well as simplify and accelerate the z-alignment process, a single-lens dynamic focusing approach was developed, using an ultrafast z-scanning lens (for example, tunable acoustic gradient of index (TAG) lens) to accomplish both in-situ surface detection and focus control quasi- simultaneously in a dual-beam setup at 140-350 kHz. The high surface detection control does not only stop to follow external surface topographies, but it also allows the detection of Princeton - 95376 interfaces as far as there is a clear refraction index contrast, which enables the optical thickness measurement of semi-transparent film. To implement both position detection and focus control for auto-focusing by a z- scanning lens, a particular laser beam setup may be adopted. Referring to FIG. 1, a system (100) is shown, where different beam paths (112, 142, and 192) are shown. In FIG. 1, a probe beam is shown as having a probe transmit path (112) and a probe return path (142). Also, a fabrication beam is shown as having a fabrication transmit path (192). For position detection and thickness measurement applications, only the probing laser beam path is needed. In FIG.1, a laser emitting device (110) is shown as the start of the probe transmit path (112). The probe laser beam may be a relatively low-power continuous wave (CW) laser. The laser may be at any appropriate wavelength for its intended purpose. In some embodiments, this may be, e.g., at a visual wavelength (e.g., generally between 380 nm to 750 nm, as understood in the art). The probe transmit path (112) is an optical path designed following the principles of confocal optics. The system may include a first lens (120). The first lens may be configured to continuously oscillate, as a function of time, a focal position of a laser from the first laser emitting device. The first lens may be a liquid tunable acoustic gradient index lens (TAG lens). In FIG.1A, the probe laser is shown as passing from the laser emitting device (110) through a first lens (120), here a varifocal TAG lens, a beam splitter (125), and a second lens (130), here an objective lens. The TAG lens is a liquid lens based on piezoelectricity and liquid resonance and is powered by a radio frequency (RF) signal from a controller (180), sometimes referred to as a TAG controller. In certain aspects, the acoustic standing wave inside the lens creates an oscillating gradient of refractive index so that the TAG lens oscillates between a converging and diverging gradient index (GRIN) lens of a diopter range at a target resonance frequency. The diopter range may be, e.g., about ± 0.5 diopter, about ± 0.6 diopter, about ± 0.7 diopter, about ± 0.8 diopter, about ± 0.9 diopter, or about ± 1.0 diopter. In some embodiment, the target resonance frequency may be 1-1000 kHz. In some embodiment, the target resonance frequency may be 10-1000 kHz. In some preferred embodiments, the target resonance frequency may be 100- 500 kHz. In some preferred embodiments, the target resonance frequency may be 130-170 kHz. In some more preferred embodiments, the target resonance frequency may be about 140 kHz. Princeton - 95376 As used herein, the term “about [a number or range]” generally refers to the number itself and / or, at its maximum extent, to values that would be rounded to that number, at the given number of decimal places. Thus, “about 1” would include values of 1, as well as values of 0.5-1.49, while “about 1.0” would include values of 1.0, as well as values of 0.95-1.049”. When defining a range, the maximum extent of the ranges may be considered, e.g., ± 1.0, this would include ± 1.0, but also ±1.049. The liquid nature of an appropriate first lens, such as a TAG lens, enables high transmittance in the visible wavelength and near-infrared wavelength (e.g., generally between 750 nm and 1.4 µm wavelengths) ranges. Unlike a conventional laser processing setup with a fixed focus at ^^0, the focal position of the probing beam zfcontinuously oscillates as a function of time ^^ with the inclusion of the TAG lens, as plotted in FIG.1B. As shown in FIG.1A, the probe beam is reflected from a surface (141) of a target object (140), which may be, e.g., one or more substrates or layers of material, etc. The target object which may be disposed on a stage (145), such as a moveable stage. The moveable stage may be moveable in the x-y plane, where the probe beam is roughly normal to the x-y plane. The optical return path (142) (i.e., the probe return path) is then directed back to the objective lens (second lens (130)). An additional objective lens (third lens (150)) (such as a 10x objective lens, with a 0.25 numerical aperture) may be used to refocus the reflected beam after passing through the beam splitter (beam splitter (125)), and direct the optical return path towards an image detection and processing module (160). The system may include a filter (155) after the third lens (150), and prior to the image detection and processing module (160). The filter may be configured to filter out-of-focus light. The filter may be, e.g., a pinhole filter. The pinhole may have any appropriate diameter. In a preferred embodiment, the diameter may be about 30 µm. In some embodiments, the diameter is no larger than 10 µm. In some embodiments, the diameter is no larger than 20 µm. In some embodiments, the diameter is no larger than 30 µm. In some embodiments, the diameter is no larger than 40 µm. In some embodiments, the diameter is no larger than 50 µm. In some embodiments, the diameter is no larger than 100 µm. The filter may be placed at the focus of the third lens (150). The image detection and processing module may include a sensor (162). The sensor may be, e.g., a photodiode. The photodiode may be a biased photodiode. The image detection and processing module may include an oscilloscope (165), or circuitry configured to measure the signal from the sensor. The oscilloscope or circuitry may Princeton - 95376 be operably coupled to the sensor. In a preferred embodiment, the signal from the sensor is measured by an oscilloscope (165). One or more processing units (171) may be operably coupled to the image detection and processing module (160). The image detection and processing module may be configured to send information related to the reflected beam to the one or more processing units (171). As used herein, the term “processing unit” generally refers to a computational device capable of accepting data and performing mathematical and logical operations as instructed by program instructions. This may include any central processing unit (CPU), graphics processing unit (GPU), core, hardware thread, or other processing construct known or later developed. The term “thread” is used herein to refer to any software or processing unit or arrangement thereof that is configured to support the concurrent execution of multiple operations. The processing unit(s) (171) may be operably coupled to memory (172), input and / or output devices (such as a keyboard, mouse, display, etc.) (173). The processing unit(s) may be operably coupled to a non-transitory computer-readable storage device (174). The non- transitory computer-readable storage device may contain instructions that, when executed by the processing unit(s), cause the processing unit(s) to perform certain steps as disclosed herein. The processing unit(s) may, e.g., be located on a remote computer (170) operably coupled to an oscilloscope. The processing unit(s) may be configured top process, in real time, information received from the image detection and processing module. For example, the information could be transferred to a computer running MATLAB® software. The one or more processing unit(s) may be configured to, collectively, perform certain steps. The steps may include receiving information from the from the image detection and processing module. The steps may include determining one or more surface positions based on a temporal response of the information. The processing unit(s) may be configured to calculate the position, thickness or refractive index of the target object based on the information related to the received reflected beam. For example, based on the temporal response of a detected PD signal (Δ ^^), one can calculate the surface position ^^Sfor the probed site. This surface position information may be useful by itself, or it may be useful for making adjustments to the target surface. For example, the measured surface position may then converted to a matching phase ^^ of the TAG lens such that ^^S(Δ ^^)= ^^f( ^^). That information may be sent to a controller (e.g., controller (180)). The controller may be configured to (i) modify a frequency of the TAG lens (120) and / or (ii) control an output of Princeton - 95376 a laser emitting device. As shown in FIG.1A, the system may include a second laser emitting device (190) (e.g., a fabricating laser source). The controller may be operably coupled to the second laser emitting device. The system may include a second beam splitter (195). The second laser emitting device (190), the second beam splitter (195), the first lens (120), the first beam splitter (125), and second lens (130) respectively form an optical path (192) (e.g., a fabrication beam transmit path) that preferably ends at the surface of the target substrate. The controller may be configured to communicate with the second laser emitting device, which may be a fabrication laser. The second laser emitting device may have any appropriate wavelength, but is preferably either a visible wavelength or a near infrared (NIR) wavelength. In a preferred embodiment, the second laser emitting device is configured to emit a NIR wavelength. In one embodiment, the second laser emitting device emits a laser at a wavelength of 800 nm. The second laser emitting device may be a pulse laser. The pulse laser may have a repetition rate of at least 500 Hz, preferably at least 750 Hz, and more preferably at least 1 kHz. The TAG controller may be configured to send a synchronized transistor-transistor logic (TTL) signal at the matching phase ^^ to trigger the second laser (such as a fabrication laser) at ^^S (Δ ^^)= ^^f ( ^^). As a result, the fabrication beam can modify the surface based on the in-situ the probing beam without physically moving neither the positioning stage (e.g., stage (145)) nor the optics (e.g., lenses (120, 130, 150), beam splitters (195, 125), etc., are all stationary). In various aspects, a method for position detecting and focus control may be provided. Referring to FIG. 2, the method (200) may include configuring (205) the system prior to operation. In some embodiments, this may include, e.g., operably coupling (205) a controller (such as a TAG controller) to a first lens (e.g., first lens (120), such as a TAG lens) and a laser source (e.g., second laser emitting device (190)) of a second laser beam in the system. The method may include sending (210) a first laser beam (e.g., from a first laser emitting device (110)) through a first lens (e.g., first lens (120))), a first beam splitter (e.g., beam splitter (125)), a second lens (e.g., second lens (130), and towards a target object (e.g., target object (140)). The method may include directing (220) a reflection of the first laser beam from the target object through the second lens and towards the first beam splitter. Princeton - 95376 The method may include directing (230) the reflection from the target object from the first beam splitter (e.g., beam splitter (125)) through a third lens (e.g., third lens (150)) and towards an image detection and processing module (e.g., module (160)). The method may include collecting (240) laser beam signal data using the image detection and processing module. The method may include using (250) the laser beam signal data to calculate the position, thickness or refractive index of the target object. The method may include performing (260) one or more tasks based on the signal data, or otherwise after collecting the laser beam signal data. Such tasks may include sending (262) a second laser beam from a laser source (e.g., second laser emitting device (190)) through a second beam splitter (e.g., beam splitter (195)), the first lens, the first beam splitter, the second lens and towards the target object. Such tasks may include using (264) a controller (e.g., controller (180), such as a TAG controller) to adjust a frequency of the TAG lens according to the signal data. Such tasks may include using (266) the controller to control the second laser beam according to an oscillation phase of the TAG lens. Such tasks may include physically marking (268) a surface (e.g., target surface (141) of the target object (140)) using the second laser beam. The disclosed surface detection method is based upon the temporal response of the detected reflected light intensity through the confocal optics. A varifocal TAG lens shapes the probing beam to a periodic scanning focal spot in z, as described by: ^^^^^^ൌ ^^ ^ ^^ cos 2 ^^ ^^ ^^ଶగ௧^^^ ௧^^ ൫ ௧^^ ^൯ ൌ ^^^ ^ ^^௧^^ cos ் (1) ^^are the scanning frequency and the period, which vary around 141 kHz and 7 μs for most examples disclosed herein. The maximum frequency for these examples goes up to 350.8 kHz. For any surface located at ^^Swithin the oscillation range of ^^f( ^^), it theoretically aligns with scanning laser focus twice per period at t1 and t2 such that: ௭^^௧భ^ୀ௭^^௧మ^ୀ௭^^ ^బ(2) ^ Therefore, two peaks in the detected signal would be observed per scanning period. FIG. 3A plots one period of z-scanning and several surfaces located at different locations (A to G) within the scanning range. FIG.3B plots the corresponding normalized PD signals for locations A to G from an experiment numbered as A1. Each surface intersects twice with zf (t). For example, the recognized double peaks for location A (solid line) correspond to the condition of zf(t) = Princeton - 95376 zA. Theoretically, the photodiode signal can also be calculated by a simplified ray transfer matrix model. Here, the peak-to-peak time interval Δt is denoted as the difference between t1and t2. ∆ ^^ ൌ ^^்^ െ ^^ଶൌି^௭ೄି௭బగcos ൬௭^ೌ^^ (3) and the ^^ ^∆ ^^^ ൌ ^^ ^ ∆௧ௌ^^^௧^^cos^^^் ^(4)it describes a linear relation between the surface position zS and measured cos ^ ^^்^ from the PD signal, which can be exploited for building a linear position sensor. The slope ^^tagand intercept z0 are both determined by the parameters of the varifocal TAG lens. Based on the mechanics of the TAG lens, the z-scanning amplitude ^^tagis linearly proportional to the driving voltage Vtagof the radio frequency (RF) signal from the TAG controller, and the z-scanning period T is determined by the driving frequency ftag of the RF signal. The measured surface position is then converted to a matching phase ^^ of the TAG lens such that such that ^^S(Δ ^^)= ^^f( ^^) and then communicated to the fabrication component of the optical system, such as the second laser emitting device (190) in FIG.1A. The TAG controller sends a synchronized transistor-transistor logic (TTL) signal at the matching phase ^^ to trigger the fabrication laser. Due to the dispersion of the TAG lens media and the difference in optical path, the two constants z0 and ^^tag generally have different values for the two laser beams (e.g., the probe beam and the fabricating beam), as denoted by z0,1, ^^tag,1, z0,2 and ^^tag,2 for the probing beam and the fabrication beam. The four constants may need to be calibrated a priori. Equaling zS and zf requires the matching phase ^^ satisfying the following condition: cos^ ^^^ ൌ௭^ೌ^,భcos ^ ^^ ∆௧ ௭బ,భି௭బ,మ்^ ^ (5) from the photodiode signal. As a result, the synchronized fabrication beam can precisely modify the probed surface without physically moving neither the positioning stage nor the optics. In a simplified case where the two beams have the same beam path and similar wavelength, the two sets of constants are approximately the same, therefore one can find, ^^ ൌ ^^∆௧(6) Princeton - 95376 In situ position detection Characterization of the in situ position detection method Multiple calibration experiments of the probing part of the disclosed setup were conducted to characterize the linear relationship as described in Eq.4. The inverse of the laser propagation direction was taken as the positive z direction. A silicon wafer is positioned on a mechanical z stage, which moves up towards the beam by a step size of 0.5 μm, with a lens (e.g., second lens (130)) (“OBJ1”) = 40x (NA = 0.65). In FIG.4, plots are shown of the measured cos(πΔt / T) and the recorded z stage position zS of three calibration experiments with different scanning amplitudes ( ^^tag). The total detection range, 2 ^^tag, is linearly proportional to the input voltage of the TAG lens Vtag. The circles represent the calibration experiment A7 with Vtag= 9 V, diamonds represent the calibration experiment A1 with Vtag = 15 V, and the “x” marks represent the calibration experiment A9with Vtag =18 V.Based on Eq. 4, a linear fit defines the calibrated surface position ^^ௌᇱ, with the fitted intercept as z0 and the slope as ^^tag. The fitted scanning range for driving voltage of 9V, 15V, and 18V is 7.40μm, 11.98μm, and 13.47 μm, respectively. FIG. 5 displays two periods of the normalized signal for three different z locations ( ^^1, z2and z3) with different driving voltages. To evaluate the accuracy and repeatability of the developed method under differentalignment and driving conditions, the error was calculated between the calibrated position ^^ௌᇱand the real position zSby ^^ ^^ ൌ ^^ௌᇱെ ^^ௌ. In FIG.6, the distribution of δz from the six repeatedcalibration experiments (A1-A6) with the same driving voltage Vtag =15V) are plotted in a boxand whisker chart. The accuracy of surface sensing is the maximum of errors (max|δz|). The linearity error ^^ is defined as the ratio of accuracy to the total z-scanning range, ^^ ൌ୫ୟ^|ఋ௭|ଶ௭^ೌ^. The linearity error in this example ranges from 1.24% to 1.95%. Variations in the tabulated z0 ^^tag, accuracy, and linearity error are possibly caused by alignment error and fluctuation of TAG lens power under liquid resonance. Based on experiments A1-A6, the average detection range (2 ^^tag) with Vtag = 15 V is 23.50 μm, with an average accuracy of 0.35 μm and an average linearity error of 1.49%. The z-scanning range of the focus depends on the optical power of both the TAG lens and the objective lens. It can be approximated ^^௧^^^ ^^^ଶ|^^ ^^|, where f0 is the focal length of the objective lens, and | ^^ ^^| represents the amplitude of the oscillating optical power of the TAG lens. As|^^ ^^|is linearly related to the driving voltage Vtag, the scanning range ^^tag islinearly proportional to Vta and ^^^ଶ. By increasing f0 and utilizing a lower magnification lens Princeton - 95376 (OBJ1), the disclosed method can be adapted for a larger detection range. In other experiments, as OBJ1 is changed from 40x to 4x, the average detection range (2 ^^tag) with Vtag=15 V is extended from 23.5 μm to 1.39 mm, with an average accuracy of 0.026 mm and an average linearity error of 1.87%. In addition, in still another calibration experiment, the TAG lens was operated at a relatively higher frequency of 350.8 kHz. By changing the driving conditions (frequency or amplitude) of the TAG lens and the optical power of the pairing objective lens, the TAG lens scanning approach is adaptable to measurements of various length scales while keeping the same level of percent error. Finally, the TAG lens scanning method can be compared with other dynamic scanning methods for surface detection, such as mechanical oscillation of a pinhole or a lens, or resonance of a microelectromechanical systems (MEMS) deformable mirror. Table 1, below, lists the response rate, detection range, accuracy (i.e., maximum of errors), and linearity error of some reported studies. The results for the TAG lens scanning method as disclosed herein are highlighted in bold. Table 1 Working principle Response Detection Accuracy Linear error Rate (Hz) Range (max| ^^ ^^|) ^^ (%) The dynamic z-scanning achieved by the TAG lens is a great substitute for any mechanical oscillation of either a pinhole, a lens, or a deformable mirror, because it substantially accelerates the surface detection process with a much higher response rate while maintaining the percent error, and is adjustable in its detection range. Profile measurement of a step surface Experimentally, a profile measurement of a non-flat, step surface was determined, where the step surface was, constructed by adhering two Si wafers of 500 μm thickness with a thin layer of optical glue with unknown thickness. The sample is positioned randomly at z = 2.2 mm for the low surface. OBJ1 was selected to be 4x to cover the entire step height in the detection range of zf (t). The sample is positioned on a stage and moves only in the x direction from 0 to 10 mm. Three sets of experiments are conducted to measure the line profile of the Princeton - 95376 sample under two calibration conditions. Using the fitted parameters from the calibration experiments in FIG. 7, the measured line profile by the TAG z-scanning is compared with an ex-situ reference measurement taken by a laser confocal microscope (Olympus Lext OLS4000). After zeroing the z location of the bottom surface, the measured profiles by TAG scanning and confocal microscope are consistent, as shown in FIG.8. Taking the measured zS from x = 5.5 mm to x = 10 mm, the average height of step h is 0.572 mm with a standard deviation of 9.57 μm by the TAG lens scanning method, versus 0.564 mm with a standard deviation of 9.71 μm by the confocal microscopy. FIGS.9A-9B plot the normalized photodiode signal for the TAG lens scanning method used here at the low surface (x = 0 mm) (9A) and the high surface (x = 10 mm) (9B). The time interval Δt is measured as 0.64T and 0.4T, respectively. Synchronous focus control The liquid resonance of the TAG lens may continuously oscillate its lens power, resulting in a continuous scanning focal position zf (t). Alternatively, the focal position can be selected discretely by synchronizing a pulsed laser with a single phase ^^ of the TAG lens. ^^^^ ^^^ ൌ ^^^^ ^^௧^^cos^ ^^^ (7) The pulsed laser is triggered by a TTL pulse elevated at the selected single phase ^^. The width of the triggering pulse is denoted by δt. δt is critical in determining both the repetition rate of synchronized pulses and the accuracy of focus control. The repetition rate of thesynchronized pulse fsync can be calculated by fsync = flaser ^ ftag ^ δt, where flaser is the laser’sinternal repetition rate. In this example, δt= 1µs, flaser= 1 kHz, ftag= 140.1 kHz, and fsync=140.1 Hz. The frequency reduction from 1 kHz to 140.1 Hz indicates that only 14% of the internal pulses are triggered in the synchronization mode. Hence, the synchronization method is more powerful when the fabrication laser has a compatible or higher response rate than the TAG lens. The focus control accuracy is defined as the axial width of the focal position when triggered at a specific phase ^^. This accuracy can be estimated by multiplying the axial scanning speed with the width δtof the triggering pulse. The axial scanning speed reaches its minimum at 0° and 180°, while it is maximized at 90°. Consequently, the axial width is also maximized at 90°. To illustrate this, ^^^^ ^^^ triggered at various phases ^^ from 0°to 180° can be characterized, and by performing a least-square fit based on Eq. 7, one can obtain ^^tag= -0.53 mm and z0= f0- 0.27 mm, with f0being the focal length of the objective lens. To account Princeton - 95376 for uncertainty from the triggering pulse width δt, an envelope of ^^^^ ^^^ can be plotted, adding a ±πftagδtterm to its phase. The accuracy of synchronous focus control is then defined as the axial width of this envelope at 90°. For ^^tag = - 0.53 mm, the maximum axial width at ^^ = 90° is ± 0.22 mm, considering δt= 1 μs. Based on the measured zSby the probing beam, a matching phase ^^ which satisfies ^^ௌൌ ^^^^ ^^^ can be calculated to trigger the fabrication beam, as described in Eq.5. In this way, the fabrication beam can effectively modify the surface based on the in situ measurement from the probing beam while neither the positioning stage nor any optical elements are physically moved in z in a single lateral scanning. Comparison of three focusing strategies The effectiveness of synchronous focus control for processing non-flat surfaces can be showcased by comparing various focusing strategies. These strategies involve only one lateral scanning in the x direction, with no motion in the z direction. For example, FIG. 10 plots the surface position zS(x) of a step surface (dotted line, with its low and high surfaces located at zs1 and zs2) and the focal position zf(x) of the laser pulses (solid line) for three focusing strategies, namely: (i) fixed focus without the TAG lens, (ii) continuous z-scanning focus without synchronization between the laser and the TAG lens, and (iii) synchronized pulses focusing at detected surface z positions. Here, the aim is to evaluate the relative amount of focused and defocused pulses out of the same number of total pulses deposited on the step surface. In this context, the term ‘defocused’ refers to cases when the pulse is focused either above or below the target surface, instead of on the target surface as intended. Each subplot in FIG.10 shows 16 deposited pulses represented by markers, with defocused pulses shown as circles, and focused pulses at zS1and zS2 shown as triangles and diamonds, respectively. Here, it is assumed that surface modification can only occur if it is located in the close vicinity of the focus. Using the first strategy, where the laser focus remains fixed and is aligned with either zS1 or zS2, only one surface can be modified. (see FIG.10 (i)) Alternatively, if one adopts a continuous z-scanning focus, both surfaces can be modified as long as all surfaces are positioned within the scanning range of zf. However, the absence of surface detection and pulse synchronization results in many continuous scanning pulses not focusing on the surface, thereby becoming ineffective. For example, in FIG.10 (ii), an oscillating focus pattern is plotted with eight pulses per period, and set z0 + ^^tag = zS1 and z0 Princeton - 95376 = zS2. The periodicity of the pulses is created by sampling the continuous z-scanning focus operating at a frequency of ftagwith a laser pulsing at an internal frequency of flaser. The mismatch between the two frequencies would generate an oscillating focus pattern. Only the one pulse at zf(0°) and the two pulses at zf(90°) and zf(270°) are focused per period, while the remaining pulses are defocused and thus do not modify the sample. In this example, a third strategy is proposed of using synchronized pulses that are only executed when the scanning zfaligns with the detected surface zS. As shown in FIG.10 (iii), both surfaces are modified within one lateral translation, and more importantly, all the deposit pulses are effectively focused. Consequently, synchronous focus control proves to be more efficient in delivering entirely focused pulses to non-flat surfaces. Laser marking on a step surface The three focusing strategies discussed above may be applied to a Si step surface, and their processing outputs may be compared. FIG.11 demonstrates the laser marking process on a sample with a step height h = 0.572 mm. The low and high surfaces are denoted as Surface 1 and 2, with their z positions at zS1 and zS2 = zS1 + h, respectively. In all experiments, the laser energy is 5 μJ / pulse. All marking lines are processed with a uniform linear translation speed of Vx in the x direction. Similar to the analysis in FIG.10, the focusing strategies are compared by evaluating the number of focused and defocused pulses on both surfaces, represented by different triangles in FIG.11. FIG. 12 provides zoom-in views of the selective marking lines A-D, displaying the percentages of focused pulses relative to all the deposited pulses on Surface 1 and 2. The scale bars in FIGS.11 and 12 are 100 μm and 30 μm, respectively. In FIG.11(i), 20 marking lines are drawn across the step. The laser focus is fixed at zf = f0when in absence of the TAG lens. The fabrication laser is pulsed at flaser= 1 kHz, and Vxis set at 0.4 mm / s. The pulse separation is dx = 0.4 μm between adjacent pulses along x and dy = 0.1 mm between adjacent lines along y. Between two adjacent lines, the sample also moves upward in the positive z direction by dz = 0.1 mm using a motorized z stage. Only three of the 20 marking lines modify each surface when the surface is located in the close vicinity of f0. Line A in FIG.12 corresponds to the case when all pulses (100%) are focused on Surface 2 but none (0%) on Surface 1, where zS2= f0and zS1= f0- h. Similarly, Line B only modifies Surface 1 (100%) but not Surface 2 (0%), where zS1 = f0 and zS2 = f0 + h. The separated z locations of the marking lines on Surface 1 and 2 suggest that a z-axis adjustment of the sample is needed to realign towards the fixed focus when translating from Surface 1 to 2, as the Rayleigh range Princeton - 95376 of the beam (< 200 μm) is smaller than the step height. This experiment represents conventional laser processing without axial detection or focus control, echoing the challenges of re- alignment as discussed herein. FIG.11(ii) and FIG.11(iii) demonstrate two marking lines with continuous z-scanning focus (Line C) and synchronized focus control (Line D). Surface 1 is placed at zS1= z0+ ^^tagfor both Line C and D to replicate the scenario in FIG. 10. In synchronous focus control, the laser focal positions are designed to align with the surface z positions, ensuring that ^^^^ ^^^^ ൌ^^ௌ^ and ^^^^^^ଶ^ൌ ^^ௌଶ ൌ ^^^^^^^^^ ℎ. Here, the position of Surface 1, ^^ௌ^ ൌ ^^^ ^ ^^௧^^,corresponds to a ^^^= 0°. Using ^^tag = - 0.53 mm and h = 0.572 mm, the calculated triggering phaseି^ ௭^ೌ^ ୡ୭^^థభ^ା^ 2 is ^^ଶൌ cos ൬௭^ೌ^^ ൌ 94° ^ 90°. Therefore, for Line D, when the laser is of the fabrication beam is switched from 0° to can (ii) and (iii) can mark both Surface 1 and 2 without any mechanical motion in z and within only one lateral translation. To facilitate a clear comparison between continuous z -scanning and synchronous focus control, the pulse separation dx is set to 3 μm for both Line C and D. Note that this particular value of dx was chosen solely for the purpose of ensuring an equal number of pulses are physically deposited on each line. The linear translation speed Vxis set to 3 mm / s and 0.4 mm / s due to the difference in repetition rate at flaser and fsync for Line C and D. Considering the image width of 320 μm along the x direction in FIG.12, a total of 320 / 3 ^ 106 pulses are deposited on each surface. The number of ablated spots is measured by taking central line profiles along x. For Line C, only 10% (11 pulses) and 20% (21 pulses) of the total 106 pulses are well focused on Surface 1 and 2. As explained for FIG.10, the ratio of focused pulses is attributable to the periodicity of the generated focus pattern. Since the z-scanning frequency is ftag= 140.1 kHz and the laser frequency is flaser = 1 kHz, the frequency ratio ftag / flaser creates an oscillating focus pattern with ten pulses per period. Within each ten-pulse period, only the one pulse at zf(0°) and the two pulses at zf (90°) or zf (270°) are focused on Surface 1 and 2. As a comparison, for Line D, 66% (70 pulses) and 67% (72 pulses) of the total deposited pulses are identified on Surface 1 and 2, respectively. The missing pulses (approximately 30%) are solely due to the uncertainty of the triggering signal. Experiments conducted to count the number of triggered pulses by the TAG lens controller in the absence of the TAG lens in the beam path report a similar missing pulse percentage of 30%. Ideally, all synchronized pulses can be focused onto Princeton - 95376 the measured surface without any mechanical adjustment in z if a more accurate triggering signal is applied. The comparison of the ratio of focused pulses above suggests that surface detection and focus control by synchronization provide more precise control by reducing the defocused pulses in the continuous z-scanning. This leads to two major advantages. First, the processing speed can greatly increase by wisely firing pulses only at the probed surface position. This aspect is particularly relevant for a pulsed laser with a higher repetition rate than the scanning frequency of the TAG lens. Second, the lateral resolution of laser modification is conserved in the synchronized method but may vary in the continuous z-scanning method. In FIGS.11 and 12, low pulse energy is adopted, so all defocused pulses are below the ablation threshold. In reality, however, the defocused pulse energy can be higher than the ablation threshold, leading to ablation with larger areas and shallower depth than focused pulses. Such an enlarged ablation area is detrimental to lateral resolution. Conversely, the enlarged ablation area in continuous z-scanning benefits certain applications thriving for removing more material. For instance, continuous z-scanning has been adopted in laser micro-machining for milling more materials and drilling deeper holes on a flat subtract compared to fixed-focus machining. Simultaneous position detection and focus control for auto-focusing Furthermore, the potential of this technique for auto-focusing and focus control may be explored, which requires the simultaneous implementation of in situ position detection and laser refocusing during lateral translation. This auto-focusing process necessitates coordination between multiple hardware and software components. To demonstrate this concept, one can first implement real-time detection and subsequently integrate the function of synchronous focus control for auto-focusing. In a first video (V1) capturing a real-time demonstration of the automatic position detection capabilities of the disclosed setup, the detection of periodic back-and-forth movements of the z stage was captured, the stage being programmed to move at a speed of 0.02 mm / s between z = 0 and z = 0.2 mm. Real-time measurements of the moving z stage with two different rates of acceleration and deceleration, 0.002 mm / s2and 0.1 mm / s2, were performed. Both experiments begin with z = 0.2mm and go through two cycles of motion. As the programmed z motion is terminated manually, the stage stops at z = 0.2 mm and z = 0.17 mm, respectively. FIGS.13A and 13B show the position detection with a z speed of 0.02 mm / s, and an acceleration of ±0.002 mm / s2(13A) and ±0.1 mm / s2(13B). Princeton - 95376 A second video (V2) captured real-time position detection of a step surface as the setup linearly translated along the x direction, after zeroing the stage at the bottom surface. The x stage translated from 0 mm to 7.5 mm with a speed of 0.1 mm / s. The step surface used was the same sample in FIG.8. A TAG lens frequency (ftag= 350.8kHz) was used in V2 that was higher than in other experiments disclosed in these examples. Therefore, the oscilloscope displays more than one period of oscillation within its acquisition time of 10 μs. A screenshot of the final measured surface position against time at the end of each measurement is shown in FIG. 13C. The plot shows the detection performance throughout the process. Real-time in situ position detection and simultaneous focus adjustment were implemented as a demonstration for auto-focusing on a two-step surface. The two-step surface is constructed by adhering three pieces of silicon wafers together. The objective lens used in the dual-laser beam path is a 10x objective lens. Immediately after turning on the probing beam, a local calibration experiment was conducted by mechanically shifting the z stage in increments of 0.05 mm and acquiring real-time signals from the oscilloscope. A calibration curve similar to those previously discussed is obtained, yielding two fitting parameters: z0,1 = 1.51 mm and ^^tag,1= - 0.38 mm. The subscript 1 here denotes the axial scanning parameters for the probing beam. Subsequently, we turn on the fabrication beam and characterize its axial scanning parameters following the method described previously. The two parameters for the fabrication beam are z0,2 = 1.45 mm and ^^tag,2 = -0.45 mm, where subscript 2 refers to the fabrication beam parameters. Based on these two sets of calibrated parameters from the probing and fabrication beams, one can calculate the matching phase, ^^, in real-time according to the transfer equation in Eq. 5. The matching phase is then input into the TAG lens controller software to trigger the fabrication beam and focus it on the probed surface position. The TAG controller can output three channels of TTL signals at the same time. In this example, we use channel 1 (CH1) and channel 2 (CH2) to trigger the oscilloscope and the fabrication laser, respectively. FIG.14 exhibits the surface position and matching phase during the auto-focusing laser marking of the two-step surface. The three surfaces are denoted as A, B, and C. A 3D microscopy of the two-step surface showing the laser marking line across all three surfaces is also included in FIG.14, indicating auto-focusing laser processing without any z stage motion. In the video, process-generated plasma using a laser pulse energy of 5 μJ was observed. Throughout the laser fabrication, the detected signal was monitored in real-time and it was found that the plasma interference is insignificant and negligible. However, under high laser Princeton - 95376 fluence irradiation, process-generated plasma may cause strong interference in the detected signal. To minimize plasma interference, one can employ time-gated detection by synchronizing the photodetector to measure the signal at specific delays after the fabrication laser pulse and plasma generation. Another option is to utilize polarization or spectral filtering, which allows selective detection of only certain polarized or wavelength components of the signal and effectively suppresses the components corresponding to the plasma emission. Moreover, additional signal processing techniques, such as background subtraction or deconvolution analysis, can be used to separate the desired peaks from the plasma interference. The example real-time demonstration achieves a response rate exceeding 1 Hz. However, this is significantly limited by the relatively simple hardware and software implementation used. It is envisioned that the position data collection and focal control could be completed within a single scanning period of the TAG lens, enabling the method to instantaneously track surface topology without mechanical movement within two periods of z- scanning. For instance, it is envisioned that when operating the TAG lens at a frequency range of 140–350 kHz, the auto-focusing system could reach a maximum response rate of, e.g., between 70 and 175 kHz. In various aspects, the disclosed concepts can be utilized as part of a method for surface detection and thickness measurement based on dynamic axial scanning by an ultrafast varifocal lens. The adopted varifocal lens is a TAG lens, a liquid acoustic lens that periodically shifts the focal position at an ultrafast frequency of 140 kHz. The z locations of multiple film surfaces can be detected in one scanning period of the TAG lens without any axial mechanical motion. The film thickness can be measured from the z position of the detected surfaces. Furthermore, the refractive index can be deduced from the confocal distance between the top and bottom surfaces. An experimental setup according to FIG. 15 is utilized, similar to that of FIG.1A, but where no second laser emitting device (190) or second beam splitter (195) was utilized. In general, a system (1600) may include a dynamic z-scanning lens (e.g., first lens (120), such as a TAG lens) configured to be operably coupled to a microscope (1610) in a laser transmit path (e.g., probe transmit path (112)) of a laser emitting source (e.g., first laser emitting device (110)) of the microscope. The system may include a controller (180) (which may include one or more processing unit(s) (1630)) operably coupled to the z-scanning lens. The controller may be configured to modify a frequency of the dynamic z-scanning lens. The system may include a signal detection module (1620) configured to be operably coupled to the microscope. The signal detection module (1620) may include a sensor (162), such as Princeton - 95376 photodiode detector, configured to receive light from the laser emitting source after passing through the dynamic z-scanning lens and reflecting off at least one surface (e.g., surface (141)). The system may include a non-transitory computer-readable storage device (1631) containing instructions that, when executed by the processing unit(s) (such as a processing unit in the controller), causes the processing unit(s) to, collectively, modify the frequency of the dynamic z-scanning lens, and determine one or more surface positions, thickness, and refractive index based on a temporal response of the information, as disclosed herein. The TAG lens is powered by a radio-frequency signal (RF in) from the TAG controller, which drives the liquid resonances in the lens and creates an oscillating gradient of refractive index that shifts the laser focus periodically. The oscillating laser focus can be described by a function of time according to Equation 1. In this example, the driving frequency of the RF signal is around 140 kHz. The value of ^^tagis determined by the optical power of the electrically tunable TAG lens and the adjacent objective lens. The probed surface needs to be positioned within the scanning range of as zf(t), such that its position zScan be measured based on the temporal response of the reflected light under dynamic axial scanning, as disclosed herein. In brief, in each scanning period, the scanning focus aligns twice with any reflective surface located within its scanning range; thus, the acquired PD signal has double peaks. If one measures the time interval between the detected double peaks as Δ ^^, the surface position zS can be expressed by Equation 4. Equation 4 can be considered to describe a position sensor to determine the axial position of a single surface. In addition, the developed method can be configured to detect multiple surfaces with an index contrast. FIG.17 plots the rays reflected by surfaces of a thin film, showing the bottom surface located in red, and the top surface in blue. The thickness of the film ^^ is the distance between the top surface ( ^^2) and the bottom surface ( ^^b). During axial scanning, since each surface intersects twice with zf(t) per period, in total, four peaks can be detected in the PD signal, as displayed in FIG. 18A. The acquired signal in FIG. 18B is an example taken from an experiment measuring PI film-A (No.1). The two symmetric peaks with relatively higher intensity correspond to the condition of zf (t) = ^^2 at the top surface, whereas the lower ones represent zf (t) = ^^1 at the bottom surface with lower back reflection. One denotes the two peak-to-peak time intervals by Δ ^^1 and Δt2 for the bottom and top surface positions in the incidentmedium (air). The obtained time intervals can be utilized to calculate ^^1and z2by Eq.4. Due to refraction, the measured lower surface ^^1is located above the real bottom surface at ^^^^. Princeton - 95376 The film thickness ^^ can be calculated from the measured top surface at ^^2if the bottomsurface position ^^ ^^ is known.^^ ൌ ^^∆௧ଶ െ ^^^ൌ ^^^^ ^^௧^^cos ^ ^^మ் ^ െ ^^^(8) the z between the detected surfaces ^^1and z2. Using geometric optics, ^^మିమ^^ ൌ ^ ^^ଶെ ^^^^^^ୟ୬^ఏ^^^ ^ୟ୬^ఏᇲ^^ൌ ^ ^^ଶെ ^^^^^ భ^ (9) of the film, ^^0 is the refractive index of the incident medium (air), and ^^ ^^1 is the numericalaperture of the probing beam when focusing at ^^1 in the incident medium. Since the opticalpower of the TAG lens (here, ~±0.5 m-1) is much smaller than the lens power of the objectivelens, NA^ ^^^ ^ NA^OBJ, ^^. ^^. , second lens ^130^^ during the oscillation of zf (t). Using the assumption of constant NA, the thickness ^^ is expressed as a function Δ ^^2, which can be acquired from the PD signal. ∆௧మ∆௧భ√^మି^^మ^^ ൌ ^^௧^^^cos ^ ^^்^ െ cos ^ ^^்^^ (10) can be simplified as, ^^ ൌ^^^ െ ^^^ ^^బ ൌ ^^ cos∆௧మ∆௧భ^ ଶ^ ^ ^ ௧^^ ^ ^ ^^ ்^ െ cos ^ ^^்^^^బ(11) In summary, Eq.(10) and Eq. ^^ is known. Alternatively, knowing ^^band hence deducing the thickness ^^ from Eq.(8) first, one can then measure the index according to Eq.(10) or Eq.(11). In this example, for data acquisition and signal processing, the photodiode signal is first measured by an oscilloscope (Tektronix DPO2022), and then transferred in real-time to a computer running Matlab. The oscilloscope is triggered by a TTL signal sent by the TAG lens controller at the running frequency. The length of acquired waveforms is 100000 points with an acquisition time ranging from 10 ^^s to 1 ms. The acquired waveform by the oscilloscope is then transferred to Matlab using the Instrument Control Toolbox via the Virtual Instrument Standard Architecture (VISA) interface for automatic post-processing. The signal processing includes (1) moving average filtering by the movmean function to return a local 500-point mean Princeton - 95376 value, and (2) peak detection by the findpeaks function with a defined minimum peak prominence of 0.0001. One can then obtain the time interval from the identified peaks and subsequently calculate the surface position, thickness, and refractive index based on thecalibrated ^^0 and ^^tag.Currently, the disclosed process adopts an ultrafast liquid z-scanning lens called the TAG lens. As disclosed herein, the optical power of the adopted TAG lens is typically adjustable around, e.g., ^0.5-1 diopter and typically operates at 140-350 kHz. Any alternative z-scanning lens with more optical power or higher frequency can be used under the same principle / methods of the approach disclosed in this section. In this example, the constructed position sensor was first characterized for detecting a single surface. In two characterization experiments (i.e., calibration i and ii), a silicon wafer was positioned on the sample stage moving in z with a step-wise pitch of 0.5 ^^m. The power of the probing laser beam is 0.2 W. The corresponding time interval is measured and plotted as cos(πΔt / T) in the primary y-axis in FIGS. 19A and 19B. According to Eq. (4), a linear regression fit between the surface position ^^S and the measured cos(πΔt / T) is plotted in a black dashed line. The secondary axis plots the error δz between the fitted and real values of ^^S and δz < ± 0.3 ^^m. FIGS.19C and 19D plot the PD signals for three different z locations at ^^1, ^^2, and ^^3for calibration i and ii, showing double peaks that are separated with different time intervals. The thickness of opaque or non-reflective samples can be determined by stacking a reflective layer on top of the sample. Next, one can demonstrate the thickness measurement of a semi-transparent polyimide (PI, HD MicroSystems, PI 2525) film by detecting its top and bottom surfaces simultaneously in one axial scanning period. PI films are prepared by spin-coating and baking (300 C for 1 h) on a microscope slide of 1 mm thickness. Both films are measured with a calibrated ^^tagof 7.40 ^^m, as previously disclosed. In FIGS.21A-21B, the acquired time intervals Δ ^^ / ^^ (21A) and surface positions (21B) of the bottom surface ( ^^1) and the top surface ( ^^2) of the film (PI film-A) for five experiments are plotted, No.1 to 5. The sample stage moves down by 0.5 ^^m each step for No.1 to 5. See, e.g., FIG.20. Two linear fits with slopes of -0.489 and -0.482 are shown for the measured ^^2and ^^1, which appropriately depicts the ^^ movement pitch of -0.5 ^^m. The error bars on the acquired time intervals are taken from 140 repeated measurements within an acquisition time of 1 ms. Similarly, one can also measure the thickness of another prepared polyimide film (PI Princeton - 95376 film-B), where two repetitive measurements are conducted between each sample movement from No.1 to 3 (see FIGS.21C and 21D). Using Eq. 4 and taking ^^= 1.70 from the datasheet of polyimide, one can plot the calculated thickness ^^ of the two prepared films in FIGS.21E and 21F. The average thickness is 14.481 ^^m with a standard deviation of 0.420 ^^m for PI film-A (21E) and 17.082 ^^m with a standard deviation of 0.171 ^^m for PI film-B (21F). The PD signals of all experiments in Fig. 3 are included in Fig.S2 of Supplement 1. One can compare the measurement results of PI film- A by dynamic scanning method to reference measurements by ellipsometry (Woollam M-2000) and confocal microscopy (Olympus LEXT OLS4000, 50× objective lens) in Table 2, below, showing the consistency of three methods. A B-spline model for the absorbing film fits the ellipsometry data. Table 2. Comparison of three methods measuring the thickness of PI film-A Methods Ellipsometry Confocal Microscopy TAG Lens Scanning thickness d (µm) 14.033 14.492 14.481 The curve fitting error bar in the table. As a reference, the refractive index modeled by ellipsometry is 1.71 at 532 nm. The response rate is recorded as the inverse of the ellipsometry measurement time, excluding the curve fitting processing time. The height of the confocal image is taken by a step-wise ^^-scan with a pitch of 1 ^^m for 35 steps. Two line profiles, each with 1024 pixels in length, are taken for the top and bottom surfaces of the film to measure its thickness. The response rate of confocal microscopy is calculated by taking the inverse of the ^^ movement time (=10 s), excluding the image stacking processing time. Finally, the response rate of the dynamic scanning method is recorded as the scanning frequency of the TAG lens (140 kHz), where the signal acquisition and peak detection processing time were excluded. Comparing these three methods, the thickness measurement by dynamic scanning has a comparable error bar with the line profiles taken by the confocal microscopy but is much quicker in response rate. Since the PI films are coated on microscope slides and mounted on the ^^ stage, values of ^^bare unknown from the stage position. Therefore, the refractive index of the sample needs to be known prior to using the dynamic scanning method. However, the refractive index can be simultaneously measured if incorporating additional interferometry in the setup. Princeton - 95376 It is envisioned postulate that the dynamic beam shaping of varifocal lenses, such as a TAG lens, can also substitute the mechanical axial motion of the reference mirror in interferometry. Thickness and index measurement of transparent materials To further validate the disclosed method in measuring both thickness and refractive index, additional transparent materials, i.e., a thin glass substrate (Schott D263, Edmund Optics, thickness= 0.40±0.05 mm) and a sapphire plate (Meller Optics, thickness= 0.030±0.002 inch), are characterized. Since the thickness of these plates exceeds the scanning range of 7.4 ^^m as calibrated previously, the setup was modified, switching out a 40x objective lens with a lower-magnification objective lens (10 x, NA=0.25). Due to the high transmittance (up to 91 %) of the samples at 532 nm, the energy of the probing beam is increased to 0.35 W. The newly characterized scanning amplitude ^^^^ ^^ ^^is found to be 0.300 mm and 0.311 mm for two calibration experiments iii and iv, as shown by the calibration curve in FIGS. 22A and 22B. The two calibration experiments are conducted under slightly different axial scanning frequencies at 138735 Hz and 138722 Hz. The ^^ pitch between the calibration data points is 0.05 mm. The position detection error ^^ ^^ does not exceed±15 ^^m. FIG. 22C exhibits the measured surface positions of the bottom surface in the air ( ^^1) and the top surface ( ^^2) of the glass sample for five experiments, No.1 to 5. The sample stage moves up by 0.05 mm for No.1 to 5, as indicated by the slopes of the linear fits. Since the sample plates are indirect contact with the stage, the position of the bottom surface ( ^^ ^^) is recorded as the ^^ position of the stage. Thus, ^^ ^^ is -0.2 to 0 mm for No.1 to No.5. Positions of ^^1 and ^^2 are obtained from the identified two pairs of double peaks from the detected signal. In FIG. 22D, five example signals showing identified peaks are taken when ^^^^is positioned between -0.3 mm to 0.1 mm. When the sample gradually shifts upwards within the range of the scanning focus, the time interval between the two pairs of double peaks (in triangles) decreases, as shown by the cartoon and the corresponding signals. Eventually, double peaks merge when the sample approaches the limits of the scanning range, as indicated by circular markers. For the thin glass sample, the top surface peaks merges when the sample is elevated at ^^ ^^= 0.1 mm, and the bottom surface peaks merge at ^^ ^^= -0.3 mm. Since our experiments are conducted with an axial pitch of 0.05 mm, the recognized ^^ ^^ region showing signals with quadruple peaks is approximately to be between ^^^^= -0.25 mm to ^^^^= 0.05 mm. For the Princeton - 95376 sapphire plate, signals with quadruple peaks are identified within a narrower ^^ range (between ^^ ^^ = -0.5 mm to ^^ ^^ =-0.3 mm) due to its higher thickness. Merging of the peaks in the detected signal limits the available sample positioning range. In perfect condition, the merging of the double-peak pair happens at the exact extreme values of the scanning range. The available positioning range, defined as the axial range of ^^ ^^ where the quadruple peaks are present, should equal to the total axial scanning range (2 ^^ ^^ ^^ ^^) minus the confocal distance between the top and bottom surface of the film, i.e., 2 ^^ ^^ ^^ ^^ − ( ^^2 − ^^1). This formulation is calculated to be 0.34 mm and 0.21 mm for the glass and sapphire samples, which approximate the experimental findings from the signals in FIG.22D. However, the bandwidth of the signal can narrow the available positioning range of ^^ ^^ and limit both the maximum and minimum detectable distance of ^^2 − ^^1. Based on a raytracing model, the bandwidth of the signal is found to be directly related to the optical power of the adopted objective lenses. A direct estimation of the bandwidth of the signal can be obtained from the endpoints of the calibration curves in FIGS.19A, 19B, 22A, or 22B: within roughly 90% of the scanning range, double peaks and hence the surface position can be identified. Hence the maximum detectable distance of ^^2 − ^^1 in our setup is 2 ^^ ^^ ^^ ^^ × 90% = 1.8 ^^ ^^ ^^ ^^. Consequently, the available positioning range is now modified to 1.8 ^^ ^^ ^^ ^^ − ( ^^2 − ^^1). Generally, if the merging of peaks in the detected signal first occurs at the ^^ ratio of ^^^^ ^^ ^^, the maximum detectable distance would be 2 ^^ ^^^^ ^^ ^^. At this upper limit of the detectable distance, there is only one unique positioning configuration to obtain two pairs of double peaks and measure two surfaces within one period of axial scanning. Moreover, the signal bandwidth also determines the lower limit of the detectable distance. Based on the endpoints of the calibration curves, the minimum value of Δ ^^ / ^^ between the two closest peaks without merging is cos−1( ^^) / ^^. Therefore, we can assume that adjacent peaks with a time interval Δ ^^ smaller than cos−1( ^^) ^^ / ^^ are considered as merged. Considering a first surface recognized by a double-peak pair with a time interval of Δ ^^, the axial width of the detectable distance from this surface can be expressed as, షభ ష^^ ൈ cosగ∆௧െ ୡ୭^ ^^^ െ c గ∆௧ ୡ୭^భ^^^ ^ି^ గ∆௧ ௧^^^ ^ ^ os ^ ^ ^^ ൌ 2^ sin ^ ^ which is ଶthe detectable distance between the top and bottom surfaces can be estimated to be ^^ ^^ Princeton - 95376 FIG. 22D includes a conceptual cartoon showing the upper and lower limit of the detectable distance. For our system, ^^ is approximately 0.9 from the endpoints of the calibration curves. Thus, the detectable distance range is 0.45 ^^^^ ^^ ^^to 1.80 ^^^^ ^^ ^^. Plugging the values of ^^^^ ^^ ^^for the 40x and 10x setup into Eq.12, one can calculate the detectable distance range is 3.31-13.32 ^^m and 0.13-0.54 mm, respectively. The samples’ thickness and index can be measured simultaneously if the quadruple peaks are present in the detected signal. The thickness of the sample can be measured according to Eq.8, as plotted in FIG.22E. The error bar of the measured thickness ^^ is represented by the standard deviation of the measured top surfaces ^^2. Additionally, values of the refractive index are deduced from the measured thickness using Eq. 10. Average values of the measured ^^ and ^^ are tabulated in Table 3, below, compared with the contact thickness measurement by a digital caliper and values of refractive index from the data sheets of samples. Note that our conventional optical microscopy cannot resolve the top surfaces of these highly transparent samples. This suggests that including an additional axial scanning module would potentially modify the confocal microscopy for more effective thin film metrology.

Claims

Princeton - 95376 What is claimed is:

1. A system for in situ position detection, thickness and refractive index measurement, and focus control, comprising: a first laser emitting device, a first lens, a first beam splitter and a second lens respectively forming an optical path; the second lens, the first beam splitter, a third lens, and an image detection and processing module respectively forming an optical return path, the image detection and processing module comprising a photodiode; wherein the second lens is configured to continuously oscillate, as a function of time, a focal position of a laser from the first laser emitting device; wherein the image detection and processing module is configured to: receive a reflected beam; and send information related to the received reflected beam to one or more remote processing units; and wherein the one or more remote processing units are, collectively, configured to: receive the information; and determine one or more surface positions based on a temporal response of the information.

2. The system of claim 1, further comprising a filter configured to remove out of focus light disposed between the third lens and the photodiode.

3. The system of claim 1, further comprising a target object forming an end of the optical path and a beginning of the optical return path.

4. The system of claim 3, wherein the image detection and processing module further comprises an oscilloscope coupled to the photodiode.

5. The system of claim 4, wherein the one or more remote processing units includes at least one processing unit within a computer operably coupled to the oscilloscope.Princeton - 95376 6. The system of claim 5, wherein the computer is configured to calculate the position, thickness or refractive index of the target object based on the information related to the received reflected beam.

7. The system of claim 1, wherein the first lens is a liquid tunable acoustic gradient index lens (TAG lens).

8. The system of claim 7, wherein the TAG lens is coupled to a TAG controller, said TAG controller configured to modify a frequency of the TAG lens; and control an output of a laser emitting device.

9. The system of claim 8, further comprising: a second laser emitting device and a second beam splitter; wherein the second laser emitting device, the second beam splitter, the TAG lens, the first beam splitter, and second lens respectively form an optical path.

10. The system of claim 9, wherein the second laser emitting device is coupled to the TAG controller.

11. A method for position detecting and focus control, the method comprising: sending a first laser beam through a first lens, a first beam splitter, a second lens, and towards a target object; directing a reflection of the first laser beam from the target object through the second lens and towards the first beam splitter; directing the first laser beam from the first beam splitter through a third lens and towards an image detection and processing module; collecting laser beam signal data using the image detection and processing module; and using the signal data to calculate the position, thickness or refractive index of the target object.

12. The method of claim 11, wherein the first lens is a TAG lens.Princeton - 95376 13. The method of claim 11, further comprising sending a second laser beam from a laser source through a second beam splitter, the first lens, the first beam splitter, the second lens and towards the target object.

14. The method of claim 13, further comprising operably coupling a TAG controller to the TAG lens and the laser source of the second laser beam.

15. The method of claim 14, further comprising using the TAG controller to adjust a frequency of the TAG lens according to the signal data.

16. The method of claim 15, further comprising using the TAG controller to control the second laser beam according to an oscillation phase of the TAG lens.

17. The method of claim 13, further comprising physically marking a surface using the second laser beam.

18. A system, comprising: a dynamic z-scanning lens configured to be operably coupled to a microscope in a laser transmit path of a laser emitting source of the microscope; a controller operably coupled to the z-scanning lens, the controller configured to modify a frequency of the dynamic z-scanning lens; a signal detection module configured to be operably coupled to the microscope, the signal detection module comprising a photodiode detector configured to receive light from the laser emitting source after passing through the dynamic z-scanning lens and reflecting off at least one surface.

19. The system of claim 18, wherein the controller includes at least one processing unit.

20. The system of claim 19, further comprising a non-transitory computer-readable storage device containing instructions that, when executed by the at least one processing unit, causes the at least one processing unit to, collectively, modify the frequency of the dynamic z- scanning lens, and determine one or more surface positions, thickness, and refractive index based on a temporal response of the information.

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