III. 2MASS Details

3. Data Processing

e. Position Reconstruction

Position Reconstruction Technique

Table 2: B-frame to U-scan Coordinate Conversion Equations

J1-frame to U-scan coordinate conversion equations:

        USxJni = (USxJCn0 +dxJ2n +DxR1) +cos(TJ)*SXJ*(JFxJni-hw)
                                        -sin(TJ)*SYJ*(JFyJni-hw)

        USyJni = (USyJCn0 +dyJ2n +DyR1) +sin(TJ)*SXJ*(JFxJni-hw)
                                        +cos(TJ)*SYJ*(JFyJni-hw)

J2-frame to U-scan coordinate conversion equations:

        USxJni = (USxJCn0 +dxJ2n      ) +cos(TJ)*SXJ*(JFxJni-hw)
                                        -sin(TJ)*SYJ*(JFyJni-hw)

        USyJni = (USyJCn0 +dyJ2n      ) +sin(TJ)*SXJ*(JFxJni-hw)
                                        +cos(TJ)*SYJ*(JFyJni-hw)

H1-frame to U-scan coordinate conversion equations:

    USxHni = (USxJCn0 +dxJ2n +DxJ2H +DxR1) +cos(TH)*SXH*(HFxHni-hw)
                                           -sin(TH)*SYH*(HFyHni-hw)

    USyHni = (USyJCn0 +dyJ2n +DyJ2H +DyR1) +sin(TH)*SXH*(HFxHni-hw)
                                           +cos(TH)*SYH*(HFyHni-hw)

H2-frame to U-scan coordinate conversion equations:

    USxHni = (USxJCn0 +dxJ2n +DxJ2H      ) +cos(TH)*SXH*(HFxHni-hw)
                                           -sin(TH)*SYH*(HFyHni-hw)

    USyHni = (USyJCn0 +dyJ2n +DyJ2H      ) +sin(TH)*SXH*(HFxHni-hw)
                                           +cos(TH)*SYH*(HFyHni-hw)

K1-frame to U-scan coordinate conversion equations:

    USxKni = (USxJCn0 +dxJ2n +DxJ2K +DxR1) +cos(TK)*SXK*(KFxKni-hw)
                                           -sin(TK)*SYK*(KFyKni-hw)

    USyKni = (USyJCn0 +dyJ2n +DyJ2K +DyR1) +sin(TK)*SXK*(KFxKni-hw)
                                           +cos(TK)*SYK*(KFyKni-hw)

K2-frame to U-scan coordinate conversion equations:

    USxKni = (USxJCn0 +dxJ2n +DxJ2K      ) +cos(TK)*SXK*(KFxKni-hw)
                                           -sin(TK)*SYK*(KFyKni-hw)

    USyKni = (USyJCn0 +dyJ2n +DyJ2K      ) +sin(TK)*SXK*(KFxKni-hw)
                                           +cos(TK)*SYK*(KFyKni-hw)