This thesis presents the measurement of prompt diphoton production rate in proton-antiproton collisions at a center-of-mass energy of 1.96 TeV using the upgraded Collider Detector at Fermilab (CDF II). This process deserves some attention for the following reasons. The H → ?? decay mode is an important channel for the Standard Model (SM) Higgs boson searches in the low mass region (MH 130 GeV) at the forth coming LHC. In many models involving physics beyond the SM, cascade decays of heavy new particles generate a ?? signature. Some examples are supersymmetry with a light gravitino, radiative decays to a higgsino-LSP and models with large symmetry groups. The QCD production of prompt photon pairs with large invariant mass is the irreducible background to these searches. The rate is huge and requires to be quantitatively evaluated prior to any of the possible discoveries. In a hadronic collider environment such as LHC, prompt photon signals are contaminated by the production of neutral mesons which decay to multiple collinear photons. The experience of classifying background of neutral meson is very important. The process can be used to test the Next-to-Leading Order (NLO) calculation of Quantum Chromodynamics (QCD). The 4-momentum of particles in the di-photon final state can be precisely determined due to the fine energy resolution of the electromagnetic calorimeters. The imbalance in the transverse momentum of the two photons reflects the transverse motion of the colliding partons. At collider energies, most of the transverse momentum of the incoming partons can be attributed to multiple soft gluon emissions prior to the collision, of which the effect to di-photon production can be resummed by Collins-Soper-Sterman (CSS) formalism. The Tevatron data can be used to test the resummation formalisms. They have used 207 pbsup-1