In six companion papers we discuss a capability for X-ray tomographic spectrophotometry at three energy ranges to observe defects (in a general sense) in various systems using a novel X- ray optical and photometric approach. We describe new types of thin-film X-ray reflecting filters to provide energy-specific optical trains, inserted into existing X-ray interrogation systems. That is complemented by performing tomographic imaging at a few, to several, energies in each case. That provides a full tomographic and spectrophotometric analysis. Defects and inclusions can then be detected, and localized, discriminated, and classified, so that they may be dealt with by excision, and replacement with benign system elements. We analyze the principles of the technique as it leads to the design of three systems: The first operates at X-ray energies of 1 - 10 KeV. It deals with defects in microelectronic integrated circuits, which destroy the devices' electronic functionality, while they are still at the wafer stage of microelectronic device manufacture. Repair techniques can then be directed to excise the defects in situ, restore the functionality of the I/C's, and bring the effective manufacturing wafer yield to 100%. The second operates at X-ray energies of 10 - 30 keV. It deals with the defects in human tissue called tumors, which destroy the biological functionality of the organs that they inhabit. The chemical specificity and image resolution of the system will allow identification, localization, and mensuration of tumors without the need of biopsy. Then all measures necessary to plan effective therapies for the tumors. The third operates at X-ray energies of 30 - 70 keV. It deals with the defects in transportation systems which are represented by the presence of lethal objects (i.e., explosive devices) and contraband materials and objects in luggage and cargo. Steps can then be taken, for the excision of those objects, from the transportation system to restore its full functionality, guaranteeing the safe and legal passage of only those objects expected (to support the normal functions of society).