Minimum Point Method Research Articles

Quantitative analyses of cirques on the Faroe Islands: evidence for time transgressive glacier occupation

This study presents the first analysis of ice‐free cirques on the Faroe Islands using a Geographical Information System (GIS) and the Automated Cirque Metric Extraction (ACME) tool. The length, width, area, circularity, mean aspect, mean slope, and elevation range, minimum, and maximum were calculated using ACME. Cirque distance to coastline was measured using ArcGIS. A total of 116 cirques were identified. Mean cirque length is 950 m and mean cirque width is 890 m. Average cirque area is 0.8 km2 and mean elevation is 386 m a.s.l. The modal orientation of the aspect of cirques is north‐northeast, with a vector mean of 7° and mean resultant length of 0.09. Aspect data have large dispersion, which shows evidence of cloudy ablation seasons in the past. The dispersion in aspect may also be related to the time transgressive nature of glacier occupation in these cirques. Past equilibrium‐line altitudes (ELAs) of cirque glaciers reconstructed with the minimum point method resulted in a mean palaeo‐ELA of 213 m a.s.l. Positive, linear relationships are observed between palaeo‐ELA and cirque distance to coastline. There are at least two possible interpretations of this relationship: (i) that the cirque formation is dependent on pre‐existing topography with cirques forming at the head of valleys, which occurs at higher elevations further inland, and (ii) that this relationship demonstrates the importance of access to moisture for glacier survival. A combination of both interpretations is also possible. Positive linear relationships are also observed between longitude and palaeo‐ELA indicative of palaeo‐precipitation patterns along an east–west gradient. Cirques on the Faroe Islands are smaller in length and width and present at lower elevations compared to cirques located in other regions of the world. The timing of glacial occupation in these cirques is not known, and the landforms likely formed over multiple glaciations.

Laser Self-Mixing Grating Interferometer for MEMS Accelerometer Testing

A simple and robust testing system based on a laser self-mixing grating interferometer (SMGI) is proposed to determine the sensitivity of accelerometers. Self-mixing grating interference occurs when the light emitted from a laser diode is incident onto a reflective grating at a fixed angle and the first-order diffracted light returns back into the laser cavity. Frequency ratio method and minimum point method that are officially used to calibrate accelerometers are modified to make it suitable to an SMGI testing system. In order to evaluate the performance of the proposed method, the sensitivity of a commercial microelectromechanical system accelerometer was tested at different vibration frequency. The obtained results show good agreement with the sensitivity given by the manufacturer's specification. Given its stability, simplicity, and efficiency, the proposed system has the potential to be adopted as an alternative method to test accelerometers for industrial applications.

Methods for the calibration of vibration pick-ups by laser interferometry: II. Experimental verification

The regression analysis method applied for data transforming and error evaluation in the sine-approximation method (SAM) for the calibration of vibration pick-ups is experimentally verified. The new algorithm used for phase unwrapping in the SAM has also been examined. Detailed procedures for the analysis of data obtained from the SAM, the modified fringe counting method (FCM) and the minimum point method (MPM) are presented and a comparison of measurements taken has been carried out. The uncertainty of the FCM, suppressed by implementing fringe phase analysis in a single vibration cycle, is evaluated experimentally. The influence of distortions of the modulation phase signal is shown. The error budgets for all applied methods are given and compared. Expanded measurement uncertainties of about 0.2% for acceleration measurements and about 0.5% for sensitivity measurements (with a 99% confidence level) have been obtained.

Methods for the calibration of vibration pick-ups by laser interferometry: I. Theoretical analysis

A regression analysis method is applied for data transforming and error evaluation in the sine-approximation method (SAM) for the calibration of vibration pick-ups by laser interferometry. A new simple algorithm for phase unwrapping in the SAM is also proposed. To make a more valuable comparison of this modified SAM with other techniques, i.e. the fringe counting method (FCM) and the minimum point method (MPM), the resolution of the measuring system is increased by using a double optical path difference homodyne interferometer. Additionally the uncertainty of the FCM is suppressed by implementing the procedure of fringe phase analysis in the turning points of the vibration cycle. This paper presents a theoretical analysis of the above mentioned problems.