A proposed modified theodolite instrument is presented. The instrument concept, sequence of operation of measurements, and design plans are reported. The proposed instrument has a potential similar to metric photogrammetry in computing 3-D coordinates without physically touching the target point. A sliding graduated rod (arm) has been introduced to connect the upper and lower parts, each of which has a separate vertical vernier. The rod supports the theodolite head that can be extended upward an arbitrary distance, thus effectively providing a second position for the head. Appropriate angular measurements, together with the length of the extension (the rod) can be used to calculate the inaccessible distances. The instrument relies on simple trigonometric functions to measure the height of objects and the horizontal and slope distances, and to perform trigonometric leveling. Accuracy potential of the instrument has been presented based on the law of propagation of random error. The flow of operations for different measurement cases has been mathematically demonstrated. The instrument is anticipated to bypass the cost-effectiveness and technological bottlenecks between plane surveying and photogrammetric systems.
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