Stable information of a sky light polarization pattern can be used for navigation with various advantages such as better performance of anti-interference, no "error cumulative effect," and so on. But the existing method of sky light polarization measurement is weak in real-time performance or with a complex system. Inspired by the navigational capability of a Cataglyphis with its compound eyes, we introduce a new approach to acquire the all-sky image under different polarization directions with one camera and without a rotating polarizer, so as to detect the polarization pattern across the full sky in a single snapshot. Our system is based on a handheld light field camera with a wide-angle lens and a triplet linear polarizer placed over its aperture stop. Experimental results agree with the theoretical predictions. Not only real-time detection but simple and costless architecture demonstrates the superiority of the approach proposed in this paper.