The fusion of captured multi-focus radiography images using the same scene is essential for adaptation of image information. Besides, transmission of secure radiography image between practitioners with keeping all image details is a challenge. These issues are handled using three dependent goals that include fusion amongst neutron and x-ray radiography images, watermarking of fused radiography images and optimization of watermarked images. The watermarking algorithms are analyzed and evaluated under various attacks. Development of optimization technique is an essential purpose for higher robustness with acceptable imperceptibility and negligible image distortion of radiography images. Backtracking search optimization algorithm(BSA) is functionalized for this target. Paired objective functions are suggested for the BSA algorithm to achieve simultaneously high robustness and imperceptibility. It is fulfilled that proficient results with respect to quality fitness function(FF) are realized with proposed ridgelet watermarking. Consequently, secure transmission of multi-focus radiography images within industrial and medical applications can be fulfilled.