Fig. 1. Distributions of the normalized average intensity and modulus of the correlation functions of a partially coherent LGpl beam with p=1, l=1, ω0=0.57  mm, and δg=0.8  mm in the focal plane. (a) I(r), (b) |μ(r,0)|, (c) |μ(r,−r)|, and (d) |μ(r,2r)|.

Fig. 2. Distribution of the normalized modulus of the DCF of a partially coherent LGpl beam for different l with p=1. (a) l=0, (b) l=1, (c) l=2, and (d) l=3.

Fig. 3. Distribution of the normalized modulus of the DCF of a partially coherent LGpl beam for different p with l=6 in the focal plane. (a) p=0, (b) p=1, (c) p=2, and (d) p=3.

Fig. 4. Experimental setup for generating a partially coherent LGpl beam and measuring the correlation functions. NDF, neutral density filter; BE, beam expander; L1, L2, L3, thin lenses; GAF, Gaussian amplitude filter; CA, circular aperture; PC1, PC2, personal computers.

Fig. 5. Schematic for the transformations of the intensity matrix. The matrices with green, yellow, and red elements denote the intensity matrix In(x,y), the first sub-matrix In′(x′,y′), and the second sub-matrix In′(2x′,2y′), respectively.

Fig. 6. Experimental results of the average intensity and square of the normalized modulus of different correlation functions of the generated partially coherent LGpl beam in the focal plane with p=1 and l=1. (a) I(r), (b) |μ(r,0)|2, (c) |μ(r,−r)|2, and (d) |μ(r,2r)|2.

Fig. 7. Experimental results of the square of the normalized modulus of the DCF of the generated partially coherent LGpl beam with p=1 for different l in the focal plane. (a) l=0, (b) l=1, (c) l=2, and (d) l=3.

Fig. 8. Experimental results of the square of the normalized modulus of the DCF of the generated partially coherent LGpl beam with l=6 for different p in the focal plane. (a) p=0, (b) p=1, (c) p=2, and (d) p=3.