Measuring Optical Spatial Coherence By Using A Lateral Shearing Interferometry

Optical fields are always partially coherent,while coherent and incoherent light are just the two extremes of partially coherent optical fields.In recent years,there has been much interest in partially coherent fields,which exhibit many extraordinary characteristics,such as self-healing,self-focusing,self-splitting and so on.As a fundamental property of partially coherent fields,the spatial coherence describes the correlation of the light at two points.Therefore,how to measure the spatial coherence is an important subject in the scope of partially coherent light.In this paper,we propose a modified lateral shearing interferometry based on a spatial light modulator(SLM)for measuring the spatial coherence.The lateral shearing interferometry has the feature of self-reference,and it employs interference between the object wave and its copy with a lateral displacement.Generally,the lateral shearing interferometry is employed to measure the phase of coherent fields.Besides,in fact,it can also be employed to measure the spatial coherence of partially coherent fields by means of the Fourier transform method of fringe pattern analysis.However,in most traditional lateral shearing interferometry,the lateral displacement of the object wave and its copy can be realized by the mechanically moving elements.Consequently,it may affect the experimental results.To overcome those drawbacks,we propose a modified lateral shearing interferometry for measuring the spatial coherence conveniently.The interferometry is based on a 4f system making use of a SLM.In the proposed interferometry,the diffraction grating at the input plane produces a series of diffraction orders,and the 11st and 11st copied waves can be obtained by a spatial filter.The lateral displacement of two copied waves can be realized by the composite blazing grating generated by the phase-modulated SLM at the Fourier plane of 4f system.The amount of displacement depends on the period of the blazing grating.Finally,the spatial coherence under test can be obtained by Fourier transform of the interferogram at the output plane.In addition,the spatial coherence along different directions can be measured by rotating the orientation of the blazing grating.Using the proposed system,we can measure both the modulus and phase of spatial coherence simultaneously.In this paper,we measure the spatial coherence with and without circular symmetry by the proposed interferometry.The experimental results are in agreement with the theoretical analysis,so it demonstrate the adaptability of this approach.Compared to the traditional lateral shearing interferometry,in our proposed scheme,the lateral shear amount is controlled by the SLM based on the computer without mechanically vibration.As a result,the measurement of spatial coherence will be more flexible and convenient.In addition,our scheme is based on the common-path interference technique,which makes it more resistant to the environmental disturbance.In conclusion,we believe our approach is helpful for the optical measurements in practice.