Grzegorz Kowzan

Surpassing the path-limited resolution of Fourier-transform spectrometry with frequency combs

We overcome the resolution limit of Fourier-transform spectrometry and measure instrumental line-shape-free broadband molecular spectra with lines narrower than the optical path-limited resolution. ...

Self-referenced, accurate and sensitive optical frequency comb spectroscopy with a virtually imaged phased array spectrometer

We present a cavity-enhanced direct optical frequency comb spectroscopy system with a virtually imaged phased array (VIPA) spectrometer and either a dither or a Pound-Drever-Hall (PDH) locking scheme used for stable transmission of the comb through the cavity. A self-referenced scheme for frequency axis calibration is shown along with an analysis of its accuracy. A careful comparison between both locking schemes is performed based on near-IR measurements of the carbon monoxide ν=3←0 band P branch transitions in a gas sample with known composition. The noise-equivalent absorptions (NEA) for the PDH and dither schemes are 9.9×10(-10) cm(-1) and 5.3×10(-9) cm(-1), respectively.

Frequency combs for cavity cascades: OPO combs and graphene-coupled cavities

Frequency combs can be used directly, for example as a highly precise spectroscopic light source. They can also be used indirectly, as a bridge between devices whose high precision requirements would normally make them incompatible. Here, we demonstrate two ways that a frequency comb enables new technologies by matching optical cavities. One cavity is the laser oscillator. A second cavity is a low-threshold doubly-resonant optical parametric oscillator (OPO). Extending optical referencing to the doubly-resonant OPO turns the otherwise unstable device into an extremely precise midinfrared frequency comb. Another cavity is an optical enhancement cavity for amplifying spectral absorption in a gas. With the high speed of a graphene-modulated frequency comb, we can couple a frequency comb directly into a high-finesse cavity for trace gas detection.

ELT -HIRES the High Resolution Spectrograph for the ELT: Fabry-Pérots for use as calibration sources

High resolution spectroscopy enables the detection of atmospheres of exoplanets. To reach the required radial velocity precision of about 1 m/s, calibration with even more precise sources is mandatory. HIRES will employ several calibration sources, the most important ones are an Laser Frequency Comb (LFC) and Fabry-P´erots (FP). The LFC needs to be filtered with a set of FP. One possible solution is to illuminate this set of FP with a broadband light source and use them as calibrators, when they are not used for filtering the LFC. It has been demonstrated that passively-stabilized FP can perform better than 10 cm/s per night. We give an overview of the currently used FP in different surveys and compare their individual features. For the FP which may be used in HIRES we discuss different configuration. We show that the Finesse and FSR of the FP needs to be optimized with regard to the resolution of the spectrograph and we outline how we aim to fulfill the requirements of HIRES.

Data analysis methods for laser frequency comb line position measurements with a Fourier transform spectrograph

Astrophysical calibration sources which can be used for high-precision radial-velocity spectroscopy require a calibration with even higher precision and accuracy. Calibration of these sources can be achieved with a high-resolution Fourier-Transform-Spectrograph (FTS). The precision (~ 20 m/s) of the FTS is mainly driven by its reference, often a stabilized HeNe-laser. To reach an acceptable precision, either averaging over a large number of measurements or a better reference is needed. We developed a setup including a Laser-Frequency-Comb (LFC) for referencing a high-resolution FTS. Due to the pulsed source specific evaluation methods have to be used to retrieve the spectrum properly. We extend the sub-nominal method used in absorption spectroscopy by showing an algorithm to determine the interferogram cut points from the interferogram itself, rather than calculating them from the repetition rate and reference laser wavelength. Furthermore, we show that line position errors measured from comb spectra are associated with amplitude variability and phase noise. We give an estimate of the measured line position stability for different evaluation methods (truncation, shifting, apodization, zerofilling) on scales not dominated by these errors.

Phase A: calibration concepts for HIRES

The instrumentation plan for the E-ELT foresees a High Resolution Spectrograph (HIRES). Among its main goals are the detection of atmospheres of exoplanets and the determination of fundamental physical constants. For this, high radial velocity precision and accuracy are required. HIRES will be designed for maximum intrinsic stability. Systematic errors from effects like intrapixel variations or random errors like fiber noise need to be calibrated. Based on the main requirements for the calibration of HIRES, we discuss different potential calibration sources and how they can be applied. We outline the frequency calibration concept for HIRES using these sources.

VIPA spectrometer calibration and comb-cavity locking schemes comparison for sensitive and accurate frequency comb spectroscopy

In direct frequency comb spectroscopy with a VIPA spectrometer, the resolution of the spectrometer is usually insufficient to resolve the comb modes. Thus, one can either filter the modes, reducing the density of spectral elements or cope with the inability to uniquely identify spectral elements with individual comb modes by calibrating the spectrometer itself. Here, we present a way to make use of the inherent frequency accuracy of a stabilized frequency comb to calibrate the spectrometer. We also present a comparison between two commonly used schemes to stabilize the coupling between a frequency comb and cavity resonances: the Pound-Drever-Hall locking scheme and the swept coupling scheme.

VIPA spectrometer for accurate and sensitive self-referenced frequency comb spectroscopy

We perform cavity-enhanced direct frequency comb spectroscopy with a self-referenced VIPA spectrometer. We compare PDH and dither cavity stabilization in near-IR measurements of carbon monoxide and measure absorption sensitivities of 9.9×10^-10 and 5.3×10^-9 cm^-1 respectively.

Broadband, comb-resolved, high-finesse enhancement cavity spectrometer with graphene modulator

We transmit a frequency comb through an enhancement cavity by PDH locking with a graphene modulator. We comb-resolve the 1940 to 2115 nm spectrum with stable repetition rate and offset frequency via Fourier transform spectrometry.

Broadband CO2 measurements with VIPA spectrometer in the near-infrared

The paper presents the way that colour can serve solving the problem of calibration points indexing in a camera geometrical calibration process. We propose a technique in which indexes of calibration points in a black-and-white chessboard are represented as sets of colour regions in the neighbourhood of calibration points. We provide some general rules for designing a colour calibration chessboard and provide a method of calibration image analysis. We show that this approach leads to obtaining better results than in the case of widely used methods employing information about already indexed points to compute indexes. We also report constraints concerning the technique. Nowadays we are witnessing an increasing need for camera geometrical calibration systems. They are vital for such applications as 3D modelling, 3D reconstruction, assembly control systems, etc. Wherever possible, calibration objects placed in the scene are used in a camera geometrical calibration process. This approach significantly increases accuracy of calibration results and makes the calibration data extraction process easier and universal. There are many geometrical camera calibration techniques for a known calibration scene [1]. A great number of them use as an input calibration points which are localised and indexed in the scene. In this paper we propose the technique of calibration points indexing which uses a colour chessboard. The presented technique was developed by solving problems we encountered during experiments with our earlier methods of camera calibration scene analysis [2]-[3]. In particular, the proposed technique increases the number of indexed points points in case of local lack of calibration points detection. At the beginning of the paper we present a way of designing a chessboard pattern. Then we describe a calibration point indexing method, and finally we show experimental results. A black-and-white chessboard is widely used in order to obtain sub-pixel accuracy of calibration points localisation [1]. Calibration points are defined as corners of chessboard squares. Assuming the availability of rough localisation of these points, the points can be indexed. Noting that differences in distances between neighbouring points in calibration scene images differ slightly, one of the local searching methods can be employed (e.g. [2]). Methods of this type search for a calibration point to be indexed, using a window of a certain size. The position of the window is determined by a vector representing the distance between two previously indexed points in the same row or column. However, experiments show that this approach has its disadvantages, as described below. * E-mail: A.Nowakowski@ire.pw.edu.pl Firstly, there is a danger of omitting some points during indexing in case of local lack of calibration points detection in a neighbourhood (e.g. caused by the presence of non-homogeneous light in the calibration scene). A particularly unfavourable situation is when the local lack of detection effects in the appearance of separated regions of detected calibration points. It is worth saying that such situations are likely to happen for calibration points situated near image borders. Such points are very important for the analysis of optical nonlinearities, and a lack of them can significantly influence the accuracy of distortion modelling. Secondly, such methods may give wrong results in the case of optical distortion with strong nonlinearities when getting information about the neighbouring index is not an easy task. Beside this, the methods are very sensitive to a single false localisation of a calibration point. Such a single false localisation can even result in false indexing of a big set of calibration points. To avoid the above-mentioned problems, we propose using a black-and-white chessboard which contains the coded index of a calibration point in the form of colour squares situated in the nearest neighbourhood of each point. The index of a certain calibration point is determined by colours of four nearest neighbouring squares (Fig.1). An order of squares in such foursome is important. Because the size of a colour square is determined only by the possibility of correct colour detection, the size of a colour square can be smaller than the size of a black or white square. The larger size of a black or white square is determined by the requirements of the exact localisation step which follows the indexing of calibration points [3]. In this step, edge information is extracted from a blackand-white chessboard. This edge information needs larger Artur Nowakowski, Wladyslaw Skarbek Institute of Radioelectronics, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warszawa, A.Nowakowski@ire.pw.edu.pl Received February 10, 2009; accepted March 27, 2009; published March 31, 2009 http://www.photonics.pl/PLP