1. What is the topic of your research? Why is it important to study the topic?


My research is about Optical Null Indicators for dynamic methods of angle measurements, which is essentially a comparative study of optical null indicators. This research contributes significantly to the field of Optical Metrological systems, particularly in optical angle measuring systems. The primary focus of this study was to investigate the metrological performance features of contemporary types of optical null indicators in angle measurements using a laser dynamic goniometer and to suggest ways to improve the accuracy of such measurements. This study is crucial because accurate plane angle measurements have wide applications in various fields, such as:


  • Industry: For precise positioning of parts.
  • Metrology: For the calibration of angle measuring equipment.
  • Medicine: For measuring joint mobility.
  • Military: For precise weapon aiming.


  1. Key Findings of the Research

This research was purely experimental, and the key findings are as follows:

  • For all autocollimating null indicators with slits and single photodetectors, and those with quadrant photodetectors without slits, the systematic error for each individual reflecting face is defined as the product of two angles: the vertical inclination of the face’s normal relative to the null-indicator optical axis and the angle between the quadrant photodiode’s vertical gap (analyzing slit) and the rotation axis.
  • Autocollimating null-indicators based on quadrant photodiodes allow two methods of adjusting the registering unit inclination, unlike those with antalyzing slits. The first method is based on signal formation on an oscilloscope, and the second method is based on the analysis of measurement data, with the latter being superior.
  • Statistical parameters of the reflecting surface quality, such as RMS and peak-to-valley values of surface point deviations, cannot predict the differences between angle measurements conducted with different null indicator types.
  • Two different types of null indicators contribute different levels of systematic errors (in the range of ±0.06 arc seconds) in a dynamic goniometer, even when all measurement conditions are kept constant for both types.


In general, a null indicator operates on the principle that the measurement is determined when the system reaches a state of equilibrium between the quantity being measured and a known reference or standard. In this study, the quantity being measured was the plane angle, the measuring system was a dynamic goniometer, and the reference or standard was an optical polygon.


In our system, the Null Indicator (NI) is an optical device used as part of a dynamic goniometer to set up a reference direction in space for the reflecting surface of the test object in high precision angle measurements. It triggers the reading of the angle data from the dynamic goniometer angle sensor and fixes it now when its optical axis is perpendicular to the reflecting surface of the object under study. Optical null indicators are used for measuring angles between polygon faces with dynamic goniometers and for the calibration of angle measuring equipment, while the optical polygon is used as the reference standard.


  1. How can the results of your research be utilized in practice?

Dynamic goniometric systems can currently achieve accuracies of tenths of an arc second or even finer. At this level, their primary application is in high-precision metrology. When used with angular standards (e.g., optical polygons, wedges), dynamic goniometric systems are integral to metrological processes, transferring the plane angle unit from primary standards to industrial angle measurement equipment.

As the demand for higher measurement accuracy increases, more factors affecting the measurement process need to be considered. One such factor, especially relevant at extreme accuracy levels, is the type of null indicator used and its interaction with the non-ideal reflecting surface of the standard.

Therefore, investigating the influence of the null-indicator type, along with the quality of the reflecting surface, is essential for assessing the accuracy of measurements taken with different null-indicator types. This study provides a comprehensive overview and classification of contemporary null indicators, detailing their performance and accuracy parameters.

Two methods for eliminating the systematic error caused by the misalignment of quadrant photodetectors in autocollimating null indicators are suggested and analyzed. Additionally, the study confirms the effect of reflecting surface quality on the consistency of angle measurements conducted with different types of null indicators.

Moreover, understanding the performance features of various null-indicator types will help define their measurement capabilities more precisely and identify their optimal applications, particularly in metrology institutes and industries.

  1. What are the key research methods and materials used in your research?


The main research method includes various laboratory experiments conducted on the department of Laser Measurement Instrumentation and Navigation System (LINS). Experiments involved measurements of plane angles of eight-sided optical polygon using laser dynamic goniometer with different existing types of optical null indicators. The measurements obtained from these experiments were compared with the nominal value of the optical polygon. The results of measurements obtained were analysed using origin lab software tool. The materials used in the doctoral research include documentary review such as., journal articles, conference papers, books, internet, pictures, photos, drawing etc.

IS there something else about your doctoral dissertation you would like to share in the press release?


In this doctoral dissertation, we proposed a new approach on experimental assessment of the reflecting surface topography influence on angle measurements. This is because the development of angle measuring technology, which allows to measure the angular position of the reflecting surface in space with high accuracy on the basis of optical methods, has currently led to the need to investigate factors that introduce errors of less than 0.1 arc seconds. A new method is presented. In this method, the issues concerning the influence of the non-flatness of the reflecting surface on the angular measurements are considered. The main emphasis is placed on the practical aspect of the study of the influence of this factor on measurements carried out by the autocollimation method.

A practical method to isolate angular deviations that occur due to the shift of the reflecting area of a non-planar surface is proposed taking into account multiple factors affecting autocollimation measurements. It consists in carrying out several calibrations of the optical polygon on a dynamic goniometric system with an autocollimation null-indicator at a transverse displacement of the null-indicator together with an aperture that determines the reflecting area. Processing the results of each calibration for the prism faces, the reduced angular deviations are evaluated and then their change is analyzed depending on the displacement of the null-indicator with the aperture. Although this method allows isolating the influence of the changing topography of the reflecting surface, it does not allow to register the angular deviation if it is the same for all the faces of the prism.

Contact: Dr.  Boniface E. Nyamweru, Email:, Mobile : +255 717 466 635