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Stock-based Compensation and Equity Grants - Stock-based Compensation Expense (Details) - USD ($)
$ in Thousands
3 Months Ended 9 Months Ended
Jun. 30, 2023
Jun. 30, 2022
Jun. 30, 2023
Jun. 30, 2022
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]        
Expense related to employee stock-based compensation   $ 481   $ 1,466
Expense related to director restricted stock units $ 179 162 $ 539 486
Total unrecognized expense 7,513 5,660 $ 7,513 5,660
Volatility     50.00%  
Additional Paid-In Capital        
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]        
Expense related to employee stock-based compensation   481   1,466
Expense related to director restricted stock units 179 162 $ 539 $ 486
Restricted Stock Units        
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]        
Number of restricted stock units granted (in shares)     337,578 161,485
Expected term (years)     3 years  
DLH employees        
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]        
Total unrecognized expense 7,358 5,498 $ 7,358 $ 5,498
Weighted average share based compensation expense recognition period     4 years 1 month 6 days  
Non-employee directors        
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]        
Total unrecognized expense $ 155 162 $ 155 $ 162
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)     50,367 53,510
NEO | Restricted Stock Units        
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]        
Number of restricted stock units granted (in shares)     197,174  
Volatility 50.00%      
NEO | Performance Based Restricted Stock Units (RSUs)        
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]        
Number of restricted stock units granted (in shares)     141,892  
NEO | Service Based Restricted Stock Units (RSUs)        
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]        
Number of restricted stock units granted (in shares)     55,282  
Selling, General and Administrative Expenses        
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]        
Total stock option expense $ 668 $ 643 $ 2,020 $ 1,952