从惠更斯-菲涅耳原理出发,得到了含有色差项的1/4圆光束在焦平面上的光场积分表达式(对于光束口径),以及具有不同相位延迟的4束1/4圆光束相干叠加后的光场表达式,并建立了该相干叠加场的远场的数学模型,并对光束口径为10 cm,焦距为200 cm,脉宽1 ps的实例进行了模拟,得到了单光束、4个子光束间无相差和存在相位差三种情况下的远场强度分布图.结果表明,单束1/4圆光束的远场不再中心对称,而是轴对称;当子光束间存在π相位差时远场将出现明显的焦斑分裂,因此光栅拼接应将束间相差控制在远小于π的水平上.

From the Huygens-Fresnel principle,an integral expression with the chromatic aberration was obtained of the field amplitude of a beam with a shape of a quarter of a circle.From the integral expression amplitude expressions of the coherent addition field of four such subbeams with different phase delay were acquired and a mathematic model of the field in the far field was set up.Numerical modulation was carried out for a 1 ps ultrashort pulse with a 10 cm aperture and 200 cm focal length.The far-field intensity distributions of three cases were given including single beam,four beams without phase delay and four beams with a phase delay of ^π between them.The conclusion is that the far-field pattern of a beam with a shape of a quarter of a circle is no more centrosymmetric but axis symmetric and that the focal spot is divided into two halves with a phase delay of ^π between the four beams.So the phase delay between subbeams should be much smaller than ^π during the course of grating tiling.