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Stock-based Compensation and Equity Grants - Stock-based Compensation Expense (Details) - USD ($) $ in Thousands | 3 Months Ended | 6 Months Ended
--- | --- | ---
Mar. 31, 2021 | Mar. 31, 2020 | Mar. 31, 2021 | Mar. 31, 2020
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |  |
Total unrecognized expense | $ 4,122 |  | $ 4,122 |
Selling, General and Administrative Expenses |  |  |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |  |
Total stock option expense | 386 | $ 182 | 844 | $ 384
DLH employees |  |  |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |  |
Total unrecognized expense | 3,888 |  | $ 3,888 |
Weighted average share based compensation expense recognition period |  |  | 4 years 4 months 20 days |
DLH employees | Restricted Stock Units |  |  |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |  |
Number of restricted stock units granted (in shares) |  |  | 147,431 |
DLH employees | Selling, General and Administrative Expenses |  |  |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |  |
Total stock option expense | 270 | 95 | $ 612 | 211
Non-employee directors |  |  |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |  |
Total unrecognized expense | 234 |  | $ 234 |
Non-employee directors | Restricted Stock Units |  |  |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |  |
Number of restricted stock units granted (in shares) |  |  | 63,177 |
Non-employee directors | Selling, General and Administrative Expenses |  |  |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |  |
Total stock option expense | $ 116 | $ 87 | $ 232 | $ 173

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