Glaucoma is the leading cause of irreversible blindness globally. Research indicates a disproportionate impact of glaucoma on racial and ethnic minorities. Existing deep learning models for glaucoma detection might not achieve equitable performance across diverse identity groups. We developed fair identify normalization (FIN) module to equalize the feature importance across different identity groups to improve model performance equity. The optical coherence tomography (OCT) measurements were used to categorize patients into glaucoma and non-glaucoma. The equity-scaled area under the receiver operating characteristic curve (ES-AUC) was adopted to quantify model performance equity. With FIN for racial groups, the overall AUC and ES-AUC increased from 0.82 to 0.85 and 0.77 to 0.81, respectively, with the AUC for Blacks increasing from 0.77 to 0.82. With FIN for ethnic groups, the overall AUC and ES-AUC increased from 0.82 to 0.84 and 0.77 to 0.80, respectively, with the AUC for Hispanics increasing from 0.75 to 0.79.