Objective A light field camera that is capable of capturing four-dimensional light field information through a single shot can be realized by inserting a microlens array in front of the sensor of a traditional camera. It has great potential to play important roles in many applications such as 3D measurement, flow field velocimetry, and wavefront sensing. To obtain the image information, the captured light-field information shall be decoded. The decoding process is largely based on the structural parameters of the light field camera, including the distance between the microlens array and sensor and the pitch of the microlens array. Because of the errors introduced during the manufacturing and assembling processes, using the nominal values of these parameters are not recommended; calibration of the true values and assembly errors are desired. Several studies have been conducted on the calibration of light field cameras. However, most of these studies follow the framework of the calibration method used for traditional cameras, where a complicated imaging model is built and the unknown parameters are searched using an optimization algorithm. The complexity of procedures in such methods makes them difficult to implement. Based on optical test principles, a new calibration method using simpler calibration models is proposed, which enables fast calibration.
Methods The proposed calibration method comprises two parts: calibration with the main lens and calibration without the main lens. The calibrations of structural parameters are accomplished when the main lens is mounted, and the calibration model is based on the relation that the exit pupil of the main lens is imaged by the microlens. A uniform light source is used to illuminate the pupil of the main lens to obtain calibration images. The distance between the microlens array and sensor and the pitch of the microlens array are treated as two optimized variables of an optimization model and are calculated by searching the optimal values. The calibration of assembly errors is accomplished when the main lens is removed, and the calibration model is based on the imaging feature of the microlens for object points at infinity. A collimated beam is used to illuminate the microlens array to obtain calibration images. Rotation and tilt errors are obtained by analyzing the geometry of the spot array in calibration images.
Results and Discussions A self-constructed light field camera is calibrated using the proposed method. The distance between the microlens array and sensor, for which the nominal value is 2.1300 mm, is calibrated to be 2.2738 mm. The pitch of the microlens array, for which the nominal value is 0.3000 mm, is calibrated to be 0.3001 mm. Furthermore, the distance between the microlens array and exit pupil of the main lens is calculated to be 47.7058 mm (Table 1). The rotation error between the microlens array and sensor is calibrated to be 0.1785°, which shall be corrected according to formula (2), and the pitch of microlens array is calculated to be 0.3001 mm by extracting the distance between adjacent spot centroids on the calibration image. The tilt error between the microlens array and sensor is 0.0083° and 0.0047° along the row and column directions of the sensor, respectively, and the distance between the microlens array and sensor is calculated to be 2.2719 mm based on equation (11). The relative deviation of the calibration values of the distance between the microlens array and sensor obtained from the two different methods is 0.84%. Based on the calibration data, reconstruction of the light field is executed and the rotation error is corrected. Compared with the reconstructed images before calibration, the quality of reconstructed images after calibration improved (Fig.10).
Conclusions To solve the problem of calibration of structural parameters and assembly errors of light field cameras, a calibration method based on optical test principles is proposed. A uniform light source is used to illuminate the optical pupil of the main lens, and the array of images of the optical pupil on the sensor is used for calculating the structural parameters, including the pitch of the microlens array and the distance between the microlens array and sensor. The assembly errors can be calibrated with the main lens removed and the microlens array illuminated directly by a collimated light beam. The calibration images captured for assembly error calibration can also be used for estimating the structural parameters through simple geometric analysis, which can serve as comparisons for the calibration results obtained from the method with the main lens mounted. Experiment results show that the calibrated and nominal values of structural parameters agree well with each other, indicating that the proposed calibration method is feasible.
