Dear Prof. Kurtsiefer Thank you for submitting your manuscript, referenced below, to Review of Scientific Instruments for consideration. "Multi-pulse fitting of Transition Edge Sensor signals from a near-infrared continuous-wave source" A181905 Your manuscript has been reviewed. While one reviewer recommended for publication, the other indicated that revisions were necessary prior to publication. See the reports below, which list in detail the comments of the reviewers. Please make the appropriate changes and upload your revised manuscript files using the link below. When uploading your revised manuscript, you should: - Indicate in your response letter how the manuscript has been revised to address the points raised by the reviewers. For comments or suggestions with which you do not agree, please provide a rebuttal. - Include your manuscript number in your response letter. - Upload your revised manuscript file in .doc, .docx, or .tex format with no highlighted or marked text. 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The allowed file formats for figure files include TIF, PS, EPS, JPEG, or high quality PDF. ------------------------------------------------------------------------------ Manuscript #A181905: Reviewer Comments: Reviewer #1 Evaluations: Recommendation: Publish as is Technically sound: Y New ideas: Y Just a variation of known device or technique: N Appropriate journal: Y Proper context with related work: Y Clear explanation: Y Adequate references: Y Suitable title: Y Adequate abstract: Y Significant numerical quantities: Y Clear figures with captions: Y Excessive text or figures: N English satisfactory: Y Regular Article vs Note: Regular Article Reviewer #1 (Remarks): The manuscript illustrates a signal processing algorithm to extract timing information from the electrical response of a transition edge sensor (TES) that contains up to tree overlapping detection events. The ad-hoc algorithm is described in great detail and its performance is thoroughly tested with a large set of data collected from an actual TES. This work is particularly relevant and suited for RSI. Here, in my opinion, the major selling points: 1) This is, at the best of my knowledge, the first time that a rigorous procedure to extract photon timing from a multi-event TES output signal is introduced. 2) Data analysis is rigorous and the principal sources of uncertainty are taken into account. 3) The performance is particularly impressive, especially given the relatively low computational load of the algorithm. In particular the timing resolution is comparable to the one obtainable by using a beamsplitter and two separate detectors to resolve the photons. 4) The triggering technique used makes the algorithm suitable to be implemented in real-time hardware using a DSP or an FPGA: In particular, referencing to Fig. 2 the dual Smith-trigger approach to find relevant qualifiers would allow dedicated hardware to robustly discard samples outside the temporal region between C and E, therefore requiring a very small memory footprint. Reviewer #2 Evaluations: Recommendation: Publish after minor revision Technically sound: Y New ideas: Y Just a variation of known device or technique: N Appropriate journal: Y Proper context with related work: Y Clear explanation: Y Adequate references: Y Suitable title: Y Adequate abstract: Y Significant numerical quantities: Y Clear figures with captions: Y Excessive text or figures: N English satisfactory: Y Regular Article vs Note: Regular Article Reviewer #2 (Remarks): This manuscript is very well written and the details are well explained. It introduces a signal processing method for Transition-Edge Sensors (TESs) that deals with overlapping monochromatic photon pulses. The method first uses two- level discrimination to locate pulses and derive integration time windows (section III). Then it assumes a linear detector response, and uses the integrated pulse area to calculate photon energy and therefore the photon number (section IV). Next, it forms a template by averaging multiple time-corrected single pulses, and fits the TES responses with a heuristic model based on this template (section V-A) to calculate the pulse trigger time (section V-B). The time tagging accuracy is then examined with a controlled laser source (section V-B). At last, the authors show that this method correctly estimates the second order correlation function g(2)(\Delta t) down to 150 ns level (section VI), further validating its ability. Overall, the pulse fitting method introduced by this manuscript demonstrates the ability to count photon numbers in the near- infrared regime under low signal-to-noise ratio conditions, and the ability to distinguish two photons separated by a couple hundred nanoseconds. Following are few comments that I believe can improve the quality of the manuscript: Section I: - "...... to work in different regions of the electromagnetic spectrum, from soft X-rays to telecom wavelengths." TESs are also used in the hard X-ray and even gamma-ray regime. Section IV: - The data shows good estimation up to 3 photons. A comment on the performance beyond this limit would be useful. Section V: - Equation (4): The left part has an extra ")" Section V.B: - Paragraph 3: "This matches the time accuracy expected from the simple noise/slope estimation for the leading edge of the single photon pulse, despite the over- lapping pulses." This comparison should be provided with other proofs, e.g. how the noise/slope estimation was done, or a proper reference material. Section VI: First paragraph: Although a reference was given, it might be helpful to briefly explain within the text why the author wanted to examine the second order correlation function. Section VII: Paragraph 5: In section V.B, it seems that this method is capable of handling events with 92 ns < Δt < 170 ns; and in section VI, the method seems capable down to 150 ns. In the conclusion, it is said "about 200 ns". Is there a specific reason why 200 ns is used? It is true that 150 and 200 are around the same order, but 200 seems to underestimate this method a little bit.