Pith. sign in

REVIEW 3 major objections 4 minor 45 references

Selective ionization of Rydberg atoms to reduce the energy spread of a cold atom focused ion beam

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper reports that selecting different Rydberg states for field ionization in a rubidium cold-atom focused ion beam reduces the beam energy spread from 23 to 12 electronvolts, about a 50 percent reduction.

desk verdict First in-situ demonstration of Rydberg state-selective energy-spread reduction in a cold atom FIB, with a clever Wien-filter diagnostic that still needs an independent calibration check. read the letter →

arxiv 2505.05750 v1 pith:6AUD5HLU submitted 2025-05-09 physics.atom-ph

Kaih T. Mitchell , Allan Pennings , Rory W. Speirs , Christopher J. Billington , Andrew J. McCulloch , Alexander A. Wood , Robert E. Scholten This is my paper · ORCID
classification physics.atom-ph
keywords coldatomfocusedionbeamRydbergatomsfieldionizationenergyspreadchromaticaberrationWienfilterrubidium-85Starkmapping
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper reports that choosing which Rydberg state is field-ionized in a rubidium cold-atom focused ion beam changes the beam energy spread by up to 50 percent, from 23 ± 2.9 eV to 12 ± 1.5 eV. The mechanism is the width of a state's ionization rate as a function of electric field: a Rydberg state (a highly excited, weakly bound atomic state sensitive to electric fields) whose ionization rate peaks over a narrower field range ionizes over a shorter distance in the accelerating field, so the ions are born over a narrower range of electrostatic potentials. The authors also introduce a practical way to measure energy spread by using a Wien filter already present in many commercial focused ion beam columns to blur images in one direction, then fitting the blur. The result matters because cold-atom ion sources can beat liquid-metal sources on brightness and resolution, and chromatic aberration from energy spread is the key limit once the spot is small.

What carries the argument

The load-bearing object is the ionization-rate function $\Gamma(F)$ and its width in electric field. The paper's model converts a narrow $\Gamma(F)$ into a narrow ionization-position and potential window through the cumulative-probability formula (the paper's Eq. 1) using simulated field $F(z)$ and gradient $dF/dz$; the resulting energy spread is estimated with $\Delta K \simeq eF(0)\Delta z_{20,80}$ (Eq. 2). On the measurement side, the Wien filter in the commercial column is the key device: its transverse acceleration is linear in $1 - K/K_0$ when the energy spread is small relative to the mean energy, so kinetic-energy spread becomes transverse-velocity spread and appears as one-axis image blur. A Fourier-analysis fit extracts the Gaussian blur $\sigma_x$, and a calibration factor converts it to the 20-80 energy width.

What would settle it

Measure the position along the beam axis, or the arrival-time distribution, at which ions are created while running at points A and B; if the ionization windows are both confined to the laser intersection and do not differ roughly twofold, the proposed mechanism would not explain the energy-spread reduction. A dedicated energy analyzer measurement on the same beam would also check whether the absolute offsets from the predicted values are a calibration artifact.

Watch

Extended reading notes

Core claim

The central discovery is that field ionization of Rydberg atoms can act as a state-selectable monochromator in a working focused ion beam. For an atom moving at speed $v$ through an accelerating field $F(z)$ with gradient $dF/dz$, the cumulative ionization probability is $P[F(z)] = 1 - \exp\!\left(-\frac{1}{v\,dF/dz}\int_{-\infty}^{F(z)} \Gamma(F')\,dF'\right)$, where $\Gamma(F)$ is the state's ionization rate. If $\Gamma(F)$ is sharply peaked, the window $\Delta z_{20,80}$ over which the ionization probability rises from 20% to 80% is short, and the energy spread $\Delta K \simeq eF(0)\Delta z_{20,80}$ is small. The authors measured Stark maps of $^{85}$Rb near the classical ionization threshold (the saddle-point field at which the electron can classically escape), selected two states with ionization-rate widths of 15 and 7.3 V/cm, and found the beam energy spread fell from $23\pm2.9$ eV to $12\pm1.5$ eV, a factor $1.9 \pm 0.48$, matching the predicted $2.1 \pm 0.21$ ratio. Because the two states would differ by less than 3 percent if ionization happened only inside the 16 µm laser intersection, the result also shows the atoms propagate out of the laser volume and field-ionize later, which is what lets the state-dependent rate set the energy spread.

Load-bearing premise

The mechanism works only if the excited atoms remain in Rydberg states long enough to be field-ionized after leaving the intersecting laser volume; if ionization were confined to that 16 µm laser overlap, choosing a different state would change the energy spread by less than 3 percent rather than the observed 50 percent.

Editorial extensions

If this is right

  • The same field-ionization scheme can be deployed inside a complete focused ion beam, not just a standalone source, so state-selective ionization is a viable route to reducing chromatic aberration in cold-atom ion machines.
  • With a more favorable accelerator geometry (lower field $F(0)$, higher gradient $dF/dz$) and narrower states, the model predicts energy spreads as low as a few meV, orders of magnitude below a gallium liquid-metal ion source.
  • For typical focused ion beam parameters, once $\Delta K/K$ falls below $10^{-5}$, chromatic aberration no longer limits the spot, so further reductions in energy spread would be aimed at lower beam energies and higher brightness.
  • Below-threshold Rydberg states have narrower $\Gamma(F)$ and should give still lower energy spreads, at the cost of lower ionization efficiency, a trade-off open to systematic state searches.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the mechanism depends only on the spatial extent of field ionization, the same state-selective reduction should transfer to cold-atom electron beams and to other alkali species; repeating the Wien-blur measurement on a lithium or cesium source would test that directly.
  • The measured absolute energy spreads sit 5.8 and 3.6 eV above the predictions, which hints at a fixed apparatus contribution to the width; if so, reducing charging drift and alignment instability could lower the floor even before changing states.
  • The necessity of delayed ionization links accelerator design to Rydberg lifetime: placing the laser intersection where the field gradient is highest would make the same $\Gamma(F)$ produce an even shorter ionization window, a co-design choice the paper leaves implicit.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper reports a demonstration of selective field ionization of Rydberg atoms to reduce the energy spread of a cold atom focused ion beam (CFIB). The authors measure the ionization rate as a function of electric field and laser frequency (Stark maps), identify two states with ionization-rate widths Γ(F) of 15 and 7.3 V/cm, and use a Wien filter to blur images along one axis in proportion to the beam energy spread. They report a reduction from 23±2.9 eV (point A) to 12±1.5 eV (point B), i.e., about 50%. The measured values are compared with predictions from a standard cumulative-ionization model (Eq. 1) and the potential variation in the accelerator (Eq. 2); the predicted values are 18±0.6 and 8.5±0.6 eV, respectively. The paper argues that the energy spread reduction implies that ionization occurs outside the intersecting laser volume, and discusses the prospects of further reducing the energy spread using states with narrower Γ(F).

Significance. If the central claim is valid, the work provides the first in situ demonstration of state-selective field ionization reducing the energy spread of a functional CFIB, a capability that liquid metal ion sources lack. The Wien-filter blur diagnostic is a potentially useful, low-cost method for measuring energy spread in commercial FIB columns, and the Stark-map-based prediction approach connects microscopic ionization physics to beam performance. The paper is strengthened by its use of a standard model (Eq. 1, from an external published treatment), by the independent measurement of the energy spread via image blur rather than spot-size optimization, and by the explicit comparison of measured and predicted values. However, the absolute calibration and data analysis of the Wien-filter measurement contain a significant methodological issue that affects the reported absolute energy spreads and the validation of the model, although the qualitative conclusion about the 50% reduction may survive after correction.

major comments (3)
  1. [Sec. V.C, Eq. (12), and Fig. 4(b)] The energy spread is computed using the total Gaussian blur σx at IB = 0.5 A without subtracting the baseline blur at IB = 0. At IB = 0 the Wien filter is off, so the measured σx is not caused by energy spread but by source size, aberrations, and other non-energy-spread effects, as evident in Fig. 3(c). Using the total σx therefore overestimates ΔK by a constant offset. This offset likely explains the systematic excess of the measured over predicted values in Table I (23 vs 18 eV, and 12 vs 8.5 eV, which differ by roughly a common 4–5 eV). The analysis should instead use the increase Δσx = σx(0.5 A) − σx(0), or equivalently the fitted slope dσx/dIB, together with a calibration factor appropriate to that increment. Because the measured absolute values and the model validation both rest on Eq. (12), this is a load-bearing issue that requires correction.
  2. [Sec. V.B, calibration of η] The calibration factor η = 2.02 ± 0.25 eV/px is derived from the image shift produced by a known change in the mean beam energy, under the assumption that the transfer function for the first moment (mean deflection) is identical to that for the second moment (blur). This linear assumption is plausible in the small-spread limit, but the authors do not validate it over the range of energy spreads encountered, nor do they test whether η depends on beam alignment or on the exact position of the ionization region. The systematic excess of the measured values over the predictions makes such a validation necessary. An independent check, for example using a beam energy spread analyzer or a sample with known chromatic response, would strengthen the quantitative claim.
  3. [Sec. V.C, assumption about ionization outside the laser volume] The conclusion that ionization occurs outside the intersecting laser volume is inferred from the 50% difference in measured energy spread. This inference assumes that the only difference between points A and B is the ionization-rate width Γ(F) and that all other beam properties (alignment, emittance, ionization position) are identical. The paper notes the absence of a lateral image shift when changing states, which supports a constant mean energy, but it does not rule out a state-dependent systematic in the Wien-filter measurement, such as a change in the beam's phase-space distribution at the filter. A more direct test, for example comparing the measured energy spreads with an independent diagnostic or measuring the energy spread at a third state, would make the inference more robust.
minor comments (4)
  1. [Sec. III, after Eq. (2)] The quoted prediction errors in Table I (e.g., ±0.6 eV) appear to include only the uncertainty in the Γ(F) FWHM values; uncertainties in the SIMION field gradient and in the electric-field calibration are not propagated. A short statement on the expected magnitude of these additional uncertainties would help readers judge the quality of the agreement.
  2. [Sec. V.C, paragraph on ionization position] The sentence 'The lack of observable lateral shift means that the change to beam energy was insignificant compared to the change to the energy spread' would benefit from a quantitative estimate of the smallest lateral shift that could have been detected, since the sensitivity of the correlation-based shift measurement is not reported.
  3. [Abstract and Sec. V.C] The abstract states that selecting different states changed the energy spread by 'up to 50%', but the measured values in Table I give a reduction from 23 to 12 eV, which is approximately 48%. If the baseline-subtraction correction alters the ratio, the stated percentage should be revisited.
  4. [Sec. IV] Minor typographical issues: 'principle quantum number' should be 'principal quantum number' in Sec. V.C, and the phrase 'full width at half maximum (FWHM)' is used with inconsistent capitalization in a few places.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the model predictions use independently measured Stark-map ionization-rate widths, and the central 50% reduction is measured with a separately calibrated Wien-filter diagnostic.

full rationale

The derivation chain is not circular. The beam energy spread is defined in Eq. 2 as ΔK ≈ e F(0) Δz20,80, where Δz20,80 is the 20–80% ionization-position range obtained from Eq. 1 using the measured ionization-rate distribution Γ(F). The Γ(F) FWHM values (15.0 and 7.3 V/cm) are experimentally determined from Stark maps, not extracted from the energy-spread data. The estimated ΔK values in Table I are therefore genuine model outputs, not fits to the measured Wien-filter blur. The experimental energy spreads are obtained through an independent diagnostic: the Wien-filter blur σx is converted using a calibration factor η = 2.02 ± 0.25 eV/px, which was measured by shifting the beam energy by a known amount and observing the image shift, not by using the energy-spread data itself. The measured A/B ratio of 1.9 ± 0.48 is a direct experimental result and is not forced by the model, even though it agrees with the predicted ratio. Equation 1 is attributed to Ref. [3], which includes a current co-author, but it is a standard published cumulant-ionization formula, and the paper does not rely on an unverified uniqueness theorem or on any self-citation as the sole justification for its central claim. The manuscript itself discloses that the measured energy spreads exceed the predictions by 3.6–5.8 eV and that η may be overestimated or additional systematics may exist; this is a calibration and accuracy caveat, not an indication of circularity. The inference that ionization occurs outside the laser volume also rests on the measured 50% difference rather than on a definition, so the paper's main demonstration is self-contained against an external measurement.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The predicted energy spreads use the measured Gaussian FWHM of the ionization rate for each state as input, so they are not parameter-free predictions. The Wien filter calibration factor is measured experimentally. No new physical entities are introduced. The main modeling assumptions are the constant-velocity, linear-field ionization probability model from Ref [3] and the inference that ionization occurs outside the laser interaction volume.

free parameters (3)
  • Γ(F) Gaussian FWHM for state A = 15.0 ± 0.5 V/cm
    Measured from experimental Stark map peak width; used as input to Eq. 1 to predict ΔK. This is a fitted width, not a first-principles parameter.
  • Γ(F) Gaussian FWHM for state B = 7.3 ± 0.5 V/cm
    Measured from experimental Stark map peak width for the narrower state; used as input to Eq. 1.
  • Wien filter calibration factor η = 2.02 ± 0.25 eV/px at IB = 0.5 A
    Determined by shifting beam energy and measuring image shift; used to convert measured σx to ΔK. Calibrated, not derived.
assumptions (5)
  • domain assumption Atoms move at constant velocity through a linearly varying electric field (Eq. 1).
    The ionization probability model from Ref [3] assumes constant velocity and a linear field gradient along z; used to compute Δz20,80.
  • domain assumption Field ionization is the dominant ionization mechanism and Rydberg atoms survive long enough to ionize outside the laser volume.
    The paper assumes atoms are ionized by the external field after leaving the intersecting laser volume, supported by the observed energy spread difference; Sec. III and V C.
  • domain assumption Γ(F) for the selected states is approximately Gaussian.
    The predicted ΔK in Fig. 2(c) uses Gaussian Γ(F) with FWHM from Stark maps; this is an empirical approximation, not derived from quantum defect theory.
  • domain assumption The energy spread is small compared to beam energy, justifying a first-order Taylor expansion in the Wien filter model (Eq. 6).
    Used to derive the linear mapping from energy distribution to transverse velocity.
  • domain assumption The paraxial approximation and independence of the Wien filter perturbation in emittance analysis (Eq. 10, 11).
    Used to argue the filter's effect on emittance and to justify the blur measurement.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Selective ionization of Rydberg atoms to reduce the energy spread of a cold atom focused ion beam." pith.science (2026). https://pith.science/paper/6AUD5HLU

@misc{pith2026250505750,
  author       = {Pith},
  title        = {Pith review of: Selective ionization of Rydberg atoms to reduce the energy spread of a cold atom focused ion beam},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6AUD5HLU}},
  note         = {Machine review of arXiv:2505.05750}
}
read the original abstract

The energy spread of a focused ion beam causes chromatic aberration that limits the focal spot size and resolution for imaging and fabrication. Ion beams based on photoionization of neutral atoms can have a much smaller energy spread and higher brightness than conventional liquid metal ion sources and are thus capable of higher resolution. We present a method for using selective ionization of Rydberg atoms to reduce the beam energy spread in a cold atom focused ion beam. We produce experimental maps of the ionization rate of Rubidium-85 near the classical ionization threshold, predict the energy spread of an ion beam produced from these states and demonstrate energy spread reduction in situ in a focused ion beam. We use a novel method to measure the energy spread, using only components present in many commercial FIB systems. Selecting different states changed the energy spread by up to 50%, with opportunities to further reduce the energy spread by constructing a more favorable electric field gradient and finding atomic states with better ionization characteristics.

Figures

Figures reproduced from arXiv: 2505.05750 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Schematic diagram of the CFIB system. (b) Energy level diagram showing the 780 nm excitation and 480 nm [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Sketch of the accelerator assembly, showing typ [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Examples of rubidium ion micrographs of tin [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Stark map showing two points with Γ( [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Plots demonstrating our algorithm for determining a [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

45 extracted references · 45 canonical work pages

  1. [1]

    J. J. McClelland, A. V. Steele, B. Knuffman, K. A. Twedt, A. Schwarzkopf, and T. M. Wilson, Appl. Phys. Rev. 3, 011302 (2016)

    work page 2016

  2. [2]

    L. Kime, A. Fioretti, Y. Bruneau, N. Porfido, F. Fuso, M. Viteau, G. Khalili, N. ˇSanti´ c, A. Gloter, B. Rasser, P. Sudraud, P. Pillet, and D. Comparat, Phys. Rev. A 88, 033424 (2013)

    work page 2013

  3. [3]

    Moufarej, M

    E. Moufarej, M. Vielle-Grosjean, G. Khalili, A. J. Mc- Culloch, F. Robicheaux, Y. J. Picard, and D. Comparat, Phys. Rev. A 95, 043409 (2017)

    work page 2017

  4. [4]

    A. J. McCulloch, R. W. Speirs, J. Grimmel, B. M. Sparkes, D. Comparat, and R. E. Scholten, Phys. Rev. A 95, 063845 (2017)

    work page 2017

  5. [5]

    Hahn, Ionisation of caesium Rydberg atoms for a mono-chromatic electron source for applications in elec- tron microscopy and spectroscopy , Ph.D

    R. Hahn, Ionisation of caesium Rydberg atoms for a mono-chromatic electron source for applications in elec- tron microscopy and spectroscopy , Ph.D. thesis, Univer- sit´ e Paris-Saclay (2021)

    work page 2021

  6. [6]

    R. Hahn, A. Trimeche, C. Lopez, D. Comparat, and Y. J. Picard, Phys. Rev. A 103, 042821 (2021)

    work page 2021

  7. [7]

    A. J. McCulloch, R. W. Speirs, S. H. Wissenberg, R. P. M. Tielen, B. M. Sparkes, and R. E. Scholten, Phys. Rev. A 97, 043423 (2018)

    work page 2018

  8. [8]

    Sahin, P

    C. Sahin, P. Geppert, A. M¨ ullers, and H. Ott, New J. Phys. 19, 123005 (2017)

    work page 2017

Show all 45 references
  1. [9]

    Lopez, A

    C. Lopez, A. Trimeche, D. Comparat, and Y. J. Picard, Phys. Rev. Appl. 11, 064049 (2019)

    2019

  2. [10]

    Trimeche, C

    A. Trimeche, C. Lopez, D. Comparat, and Y. J. Picard, Phys. Rev. Res. 2, 043295 (2020)

    2020

  3. [11]

    C. W. Hagen, E. Fokkema, and P. Kruit, J. Vac. Sci. Technol., B 26, 2091 (2008)

    2008

  4. [12]

    Bauerdick, L

    S. Bauerdick, L. Bruchhaus, P. Mazarov, A. Nadzeyka, R. Jede, J. Fridmann, J. E. Sanabia, B. Gila, and B. R. Appleton, J. Vac. Sci. Technol., B 31, 06F404 (2013)

    2013

  5. [13]

    Knuffman, A

    B. Knuffman, A. V. Steele, J. Orloff, and J. J. McClel- land, New J. Phys. 13, 103035 (2011)

    2011

  6. [14]

    A. V. Steele, A. Schwarzkopf, J. J. McClelland, and B. Knuffman, Nano Futures 1, 015005 (2017)

    2017

  7. [15]

    Viteau, M

    M. Viteau, M. Reveillard, L. Kime, B. Rasser, P. Su- draud, Y. Bruneau, G. Khalili, P. Pillet, D. Comparat, I. Guerri, A. Fioretti, D. Ciampini, M. Allegrini, and F. Fuso, Ultramicroscopy 164, 70 (2016)

    2016

  8. [16]

    Steele, A

    A. Steele, A. Schwarzkopf, and B. Knuffman, Microsc. Microanal. 27, 24 (2021)

    2021

  9. [17]

    ten Haaf, Ultracold Rb Focused Ion Beam , Ph.D

    G. ten Haaf, Ultracold Rb Focused Ion Beam , Ph.D. the- sis, Department of Applied Physics, Eindhoven Univer- sity of Technology (2017)

    2017

  10. [18]

    ten Haaf, T

    G. ten Haaf, T. C. H. de Raadt, G. P. Offermans, J. F. M. van Rens, P. H. A. Mutsaers, E. J. D. Vredenbregt, and S. H. W. Wouters, Phys. Rev. Appl. 7, 054013 (2017)

    2017

  11. [19]

    Xu, Applications of an Ultracold Focused Rb + Ion Beam, Ph.D

    S. Xu, Applications of an Ultracold Focused Rb + Ion Beam, Ph.D. thesis, Department of Applied Physics, Eindhoven University of Technology (2023)

    2023

  12. [20]

    Y. Li, S. Xu, T. H. Loeber, and E. J. D. Vredenbregt, Microsc. Microanal. , 817 (2024)

    2024

  13. [21]

    K. T. Mitchell, Cold atom focused ion beam with state- selective ionisation for reduced chromatic aberration , Ph.D. thesis, School of Physics, The University of Mel- bourne (2024)

    2024

  14. [22]

    Orsay Physics, www.orsayphysics.com

  15. [23]

    T. F. Gallagher, Rydberg atoms (Cambridge University Press, Cambridge, 1994)

    1994

  16. [24]

    C. A. Nicolaides, C. W. Clark, and M. H. Nayfeh, eds., Atoms in Strong Fields (Springer New York, NY, 1990)

    1990

  17. [25]

    Manura and D

    D. Manura and D. Dahl, SIMION 8.1 User Manual , Adaptas Solutions, LLC, Palmer, MA 01069 (2008), http://simion.com/

    2008

  18. [26]

    D. A. Harmin, Phys. Rev. A 30, 2413 (1984)

    1984

  19. [27]

    Comparat, Private communication (2023)

    D. Comparat, Private communication (2023)

    2023

  20. [28]

    ten Haaf, S

    G. ten Haaf, S. H. W. Wouters, D. F. J. Nijhof, P. H. A. Mutsaers, and E. J. D. Vredenbregt, Ultramicroscopy 190, 12 (2018)

    2018

  21. [29]

    Bischoff, P

    L. Bischoff, P. Mazarov, L. Bruchhaus, and J. Gierak, Appl. Phys. Rev. 3, 021101 (2016)

    2016

  22. [30]

    W. Pilz, N. Klingner, L. Bischoff, P. Mazarov, and 10 S. Bauerdick, J. Vac. Sci. Technol., B 37, 021802 (2019)

    2019

  23. [31]

    H¨ oflichet al

    K. H¨ oflichet al. , Appl. Phys. Rev. 10, 041311 (2023)

    2023

  24. [32]

    Orloff, ed., Handbook of Charged Particle Optics , 2nd ed

    J. Orloff, ed., Handbook of Charged Particle Optics , 2nd ed. (CRC Press, Boca Raton, 2009)

    2009

  25. [33]

    Reiser, Theory and Design of charged particle beams , 2nd ed

    M. Reiser, Theory and Design of charged particle beams , 2nd ed. (Wiley-VCH, Weinheim, 2008)

    2008

  26. [34]

    D. B. Branden, T. Juhasz, T. Mahlokozera, C. Vesa, R. O. Wilson, M. Zheng, A. Kortyna, and D. A. Tate, J. Phys. B: At., Mol. Opt. Phys. 43, 015002 (2009)

    2009

  27. [35]

    J. E. Barth and P. Kruit, Optik 101, 101 (1996)

    1996

  28. [36]

    Wang and Z

    Y. Wang and Z. Shao (Academic Press, 1991) pp. 177– 209

    1991

  29. [37]

    S. Xu, Y. Li, and E. J. D. Vredenbregt, Journal of Vac- uum Science & Technology B 40, 042801 (2022)

    2022

  30. [38]

    D. J. Griffiths, Introduction to electrodynamics , 3rd ed. (Prentice-Hall, New Jersey, 1999)

    1999

  31. [39]

    D. C. Joy, Y.-U. Ko, and J. J. Hwu, in Metrology, In- spection, and Process Control for Microlithography XIV , Vol. 3998, edited by N. T. Sullivan, International Society for Optics and Photonics (SPIE, 2000) pp. 108 – 114

    2000

  32. [40]

    Ishitani and M

    T. Ishitani and M. Sato, Scanning 24, 191 (2002)

    2002

  33. [41]

    Babin, M

    S. Babin, M. Gaevski, D. Joy, M. Machin, and A. Mar- tynov, J. Vac. Sci. Technol., B 24, 2956 (2006)

    2006

  34. [42]

    Brostrøm and K

    A. Brostrøm and K. Mølhave, Microsc. Microanal. 28, 469 (2022)

    2022

  35. [43]

    D. A. Steck, Classical and modern optics, http://steck. us/teaching (revision 1.7.6) (2020)

    2020

  36. [44]

    Hecht and A

    E. Hecht and A. Zajac, Optics (Addison-Wesley Publish- ing Company, 1987)

    1987

  37. [45]

    J. W. Goodman, Introduction to Fourier Optics , 3rd ed. (Roberts & Company Publishers, Englewood, Colorado, 2005)

    2005

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.