Lens-based phase retrieval under spatially partially coherent illumination—Part I: Theory

Falldorf, Claas; Agour, Mostafa; Thiemicke, Fabian; Bergmann, Ralf B.

doi:10.1016/j.optlaseng.2020.106507

Cited by 3 publications

(5 citation statements)

References 17 publications

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“…For object parts outside the focal plane, the speckle fields will shift depending on the angle of the corresponding elementary source with the observation direction, and hence the speckle fields will rapidly wash out. The maximum shift ∆x(z) in the individual (elementary) speckle fields concerning the out-of-focus distance z can be determined by [15]…”

Section: Form Measurements Based On Intensity Contrastmentioning

confidence: 99%

“…With a radius of the point spread function of the 4 f -imaging system of δx = 1.22λ f /D, with D denoting the diameter of an aperture located at the common Fourier plane, the contrast disappears at ∆x > δx. According to the heuristic contrast model we developed for phase retrieval in [15], the contrast K can be written as…”

Section: Form Measurements Based On Intensity Contrastmentioning

confidence: 99%

“…The 4 f -imaging system is essentially a spatial filter, as shown by the analysis of its transfer function, limiting the coherent modes passing its aperture [14]. Consequently, this method uses spatially partially coherent illumination to encode depth information as an intensity contrast at the output of the imaging system [15]. We have termed this distinctive approach of shape measurements based on imaging with spatially partially coherent illumination as SPICE profilometry.…”

Section: Introductionmentioning

confidence: 99%

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Extended-Aperture Shape Measurements Using Spatially Partially Coherent Illumination (ExASPICE)

Agour,

Falldorf,

Bergmann

2024

Sensors

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We have recently demonstrated that the 3D shape of micro-parts can be measured using LED illumination based on speckle contrast evaluation in the recently developed SPICE profilometry (shape measurements based on imaging with spatially partially coherent illumination). The main advantage of SPICE is its improved robustness and measurement speed compared to confocal or white light interferometry. The limited spatial coherence of the LED illumination is used for depth discrimination. An electrically tunable lens in a 4f-configuration is used for fast depth scanning without mechanically moving parts. The approach is efficient, takes less than a second to capture required images, is eye-safe and offers a depth of focus of a few millimeters. However, SPICE’s main limitation is its assumption of a small illumination aperture. Such a small illumination aperture affects the axial scan resolution, which dominates the measurement uncertainty. In this paper, we propose a novel method to overcome the aperture angle limitation of SPICE by illuminating the object from different directions with several independent LED sources. This approach reduces the full width at half maximum of the contrast envelope to one-eighth, resulting in a twofold improvement in measurement accuracy. As a proof of concept, shape measurements of various metal objects are presented.

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Section: Form Measurements Based On Intensity Contrastmentioning

confidence: 99%

Section: Form Measurements Based On Intensity Contrastmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Extended-Aperture Shape Measurements Using Spatially Partially Coherent Illumination (ExASPICE)

Agour,

Falldorf,

Bergmann

2024

Sensors

Self Cite

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show abstract

“…With the radius of the point spread function of the 4f -imaging system δx = 1.22f /D, D denoting the diameter of an aperture located at the common Fourier plane, the contrast disappears at ∆x > δx. According to the heuristic contrast model which is developed for phase retrieval in 13 the contrast K can be written as…”

Section: Form Measurements Based On Intensity Contrastmentioning

confidence: 99%

“…12 Accordingly, the method uses the spatially partially coherent illumination to encode the depth information as an intensity contrast at the output of the imaging system. 13 However, the main limitation of this approach arises from the underlying assumption that a small angle of variation of illumination is required. Such a small illumination aperture affects the axial scan resolution that dominates the measurement uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Improved 3D form profiler based on extending illumination aperture

Agour¹,

Falldorf²,

Bergmann³

2023

Optical Measurement Systems for Industrial Inspection XIII

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We recently demonstrated that the 3D shape of micro-parts can be measured using LED illumination based on contrast evaluation. The technique is based on imaging the object under test using partially coherent illumination. The limited spatial coherence of LED illumination was utilized to discriminate depth. For a fast depth scan without mechanically moving parts, an electrically tunable lens (ETL) in a 4f optical configuration is used. This approach is efficient, takes less than a second to capture all required images, is eye-safe, and offers a depth of focus of a few millimeters. However, the main limitation of the proposed approach arises from the underlying assumption that a small angle of variation of illumination is required. Such a small illumination aperture affects the axial scan resolution that dominates the measurement uncertainty. In the present paper we propose a method to overcome the main limitation of the above-mentioned profiling technique. The approach combines measurements with multiple illumination directions achieved by illuminating the object simultaneously with several independent light sources. In this way, the full-width half maximum of the contrast envelope is reduced. A tilted metallic plate is used for proof of concept.

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Fast 3D form measurement using a tunable lens profiler based on imaging with LED illumination

Agour¹,

Fallorf²,

Bergmann³

2020

Opt. Express

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We present a fast shape measurement of micro-parts based on depth discrimination in imaging with LED illumination. It is based on a 4f-setup with an electrically adjusted tunable lens at the common Fourier plane. Using such a configuration, the opportunity to implement a fast depth scan by means of a tunable lens without the requirement of mechanically moving parts and depth discrimination using the limited spatial coherence of LED illumination is investigated. The technique allows the use of limited spatially partially coherent illumination which can be easily adapted to the test object by selecting the geometrical parameters of the system accordingly. Using this approach, we demonstrate the approach by measuring the 3D form of a tilted optically rough surface and a cold-formed micro-cup. The approach is robust, fast since required images are captured in less than a second, and eye-safe and offers an extended depth of focus in the range of few millimetres. Using a step height standard, we determine a height error of ±1.75 μm (1σ). This value may be further decreased by lowering the spatial coherence length of the illumination or by increasing the numerical aperture of the imaging system.

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Lens-based phase retrieval under spatially partially coherent illumination—Part I: Theory

Cited by 3 publications

References 17 publications

Extended-Aperture Shape Measurements Using Spatially Partially Coherent Illumination (ExASPICE)

Extended-Aperture Shape Measurements Using Spatially Partially Coherent Illumination (ExASPICE)

Improved 3D form profiler based on extending illumination aperture

Fast 3D form measurement using a tunable lens profiler based on imaging with LED illumination

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