Long-Term Debt - Additional Information (Details)							3 Months Ended	9 Months Ended	12 Months Ended
	Apr. 12, 2024 USD ($)	Jun. 26, 2023 USD ($) Days $ / shares shares	Nov. 22, 2022 USD ($)	Dec. 17, 2020	Jun. 12, 2020 USD ($)	Jun. 02, 2020 USD ($) Days $ / shares shares	Jun. 30, 2023 USD ($)	Dec. 31, 2023 USD ($)	Sep. 30, 2024 USD ($)	Sep. 30, 2023 USD ($)	Sep. 30, 2022 USD ($)	Jul. 03, 2023 USD ($)	Mar. 31, 2023 USD ($)
Debt Instrument [Line Items]
Aggregate principal amount									$ 297,500,000	$ 297,500,000
Loss on extinguishment of debt										(1,333,000)
Payment on debt issuance costs									419,000	17,176,000
Proceeds from issuance of notes										210,000,000
Long-Term Debt									281,906,000	275,951,000
Debt unamortized issuance costs, net									12,817,000	17,753,000
Debt, principal amount, net									297,500,000
Senior Credit Facilities
Debt Instrument [Line Items]
Pledge equity interests in foreign subsidiaries					65.00%
Minimum liquidity									$ 75,000,000
Debt instrument, covenant description									The Credit Agreement contains certain affirmative and negative covenants customary for financings of this type that, among other things, limit our and our subsidiaries’ ability to incur additional indebtedness or liens, to dispose of assets, to make certain fundamental changes, to designate subsidiaries as unrestricted, to make certain investments, to prepay certain indebtedness and to pay dividends, or to make other distributions or redemptions/repurchases, in respect of our and our subsidiaries’ equity interests. In addition, the Credit Agreement contains financial covenants, each tested quarterly, (1) a net secured leverage ratio of not greater than 3.25 to 1.00; (2) a net total leverage ratio of not greater than 4.25 to 1.00; and (3) minimum liquidity of at least $75 million. The Credit Agreement also contains events of default customary for financings of this type, including certain customary change of control events.
Amended Senior Credit Facilities
Debt Instrument [Line Items]
Debt Instrument, interest rate description									Amendment No. 1 revised certain interest rates in the Credit Agreement. Following delivery of a compliance certificate for the first full fiscal quarter after the Amendment No. 1 Effective Date, the applicable margins for the revolving credit and term facilities is subject to a pricing grid based upon the net total leverage ratio as follows (i) if the net total leverage ratio is greater than 3.00 to 1.00, the applicable margin is LIBOR plus 3.00% or ABR plus 2.00%; (ii) if the net total leverage ratio is less than or equal to 3.00 to 1.00 but greater than 2.50 to 1.00, the applicable margin is LIBOR plus 2.75% or ABR plus 1.75%; (iii) if the net total leverage ratio is less than or equal to 2.50 to 1.00 but greater than 2.00 to 1.00, the applicable margin is LIBOR plus 2.50% or ABR plus 1.50%; (iv) if the net total leverage ratio is less than or equal to 2.00 to 1.00 but greater than 1.50 to 1.00, the applicable margin is LIBOR plus 2.25% or ABR plus 1.25%; and (v) if the net total leverage ratio is less than or equal to 1.50 to 1.00, the applicable margin is LIBOR plus 2.20% or ABR plus 1.00%. As a result of Amendment No 1, the applicable LIBOR floor was reduced from 0.50% to 0.00%.
Description of unused line fee									In addition, the quarterly commitment fee required to be paid based on the unused portion of the Revolving Facility is subject to a pricing grid based upon the net total leverage ratio as follows (i) if the net total leverage ratio is greater than 3.00 to 1.00, the unused line fee is 0.500%; (ii) if the net total leverage ratio is less than or equal to 3.00 to 1.00 but greater than 2.50 to 1.00, the unused line fee is 0.450%; (iii) if the net total leverage ratio is less than or equal to 2.50 to 1.00 but greater than 2.00 to 1.00, the unused line fee is 0.400%; (iv) if the net total leverage ratio is less than or equal to 2.00 to 1.00 but greater than 1.50 to 1.00, the unused line fee is 0.350%; and (v) if the net total leverage ratio is less than or equal to 1.50 to 1.00, the unused line fee is 0.300%.
Amended Senior Credit Facilities | L I B O R
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate				0.00%	0.50%
Credit Agreement Amendment Two
Debt Instrument [Line Items]
Debt Instrument, interest rate description									Amendment No. 2 revised certain interest rates in the Credit Agreement. The applicable margins for the revolving credit and term facilities is subject to a pricing grid based upon the net total leverage ratio as follows (i) if the net total leverage ratio is greater than 3.00 to 1.00, the applicable margin is SOFR plus 10 basis point credit spread adjustment plus 3.00% or ABR plus 2.00%; (ii) if the net total leverage ratio is less than or equal to 3.00 to 1.00 but greater than 2.50 to 1.00, the applicable margin is SOFR plus 10 basis point credit spread adjustment plus 2.75% or ABR plus 1.75%; (iii) if the net total leverage ratio is less than or equal to 2.50 to 1.00 but greater than 2.00 to 1.00, the applicable margin is SOFR plus 10 basis point credit spread adjustment plus 2.50% or ABR plus 1.50%; (iv) if the net total leverage ratio is less than or equal to 2.00 to 1.00 but greater than 1.50 to 1.00, the applicable margin is SOFR plus 10 basis point credit spread adjustment plus 2.25% or ABR plus 1.25%; and (v) if the net total leverage ratio is less than or equal to 1.50 to 1.00, the applicable margin is SOFR plus 10 basis point credit spread adjustment plus 2.20% or ABR plus 1.00%. During the covenant adjustment period, and until the delivery of a compliance certificate for the first full fiscal quarter after the covenant adjustment period, the applicable margin will be SOFR plus 10 basis point credit spread adjustment plus 3.00% or ABR plus 2.00%.
Minimum liquidity													$ 125,000,000
Maximum capital expenditures amount								$ 7,500,000
Payment of refinancing fees to lender			$ 400,000
Payment of refinancing fees to third party			$ 100,000
Credit Agreement Amendment Two | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			2.00%
Credit Agreement Amendment Two | SOFR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			0.10%
Credit Agreement Amendment Two | SOFR plus Ten Basis Point Credit Spread Member
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			3.00%
Credit Agreement Amendment Three
Debt Instrument [Line Items]
Debt Instrument, interest rate description									Total interest expense relating to the Senior Credit Facilities for the fiscal year ended September 30, 2024, 2023 and 2022 was $0.4 million, $6.7 million, $4.3 million, respectively, reflecting the coupon and accretion of the discount.
Interest expense									$ 400,000	6,700,000	$ 4,300,000
Minimum liquidity	$ 50,000,000
Maximum capital expenditures amount	$ 10,000,000
Debt instrument maturity date description									Amendment No. 3 also modified the maturity date for the Revolving Facility. The Revolving Facility matures on April 1, 2026, provided that if on any date during the period commencing on the date which is 91 days prior to the maturity date of our 2025 Notes and any indebtedness incurred to refinance such notes that matures on or prior to July 1, 2026, and ending on July 1, 2026, the maturity date of such Early Maturity Debt has not been extended to a date after July 1, 2026 and we do not hold in a segregated deposit account an amount of cash sufficient to repay and discharge the principal amount of the Early Maturity Debt at maturity, then the Revolving Facility shall mature on the date that is 91 days prior to the maturity date of the Early Maturity Debt.
Credit Agreement Amendment Three | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate	2.00%
Credit Agreement Amendment Three | SOFR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate	3.00%
Credit Agreement Amendment Three | One month SOFR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate	1.00%
Maximum
Debt Instrument [Line Items]
Percentage of the remaining cash flow of original instrument									10.00%
Maximum | Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio									4.25
Net secured leverage ratio									3.25%
Maximum | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net secured leverage ratio								4.25%
Maximum | Credit Agreement Amendment Three
Debt Instrument [Line Items]
Net secured leverage ratio	3.00%
1.50% Convertible Senior Notes Due 2028
Debt Instrument [Line Items]
Aggregate principal amount		$ 190,000,000							$ 122,500,000	122,500,000
Payment on debt issuance costs									2,400,000
Debt instrument convertible, if-converted value of the Notes less than its principal amount									$ 113,000,000	$ 61,200,000
Debt instrument, interest rate		1.50%							1.50%	1.50%
Debt Instrument, option to purchase additional principal amount												$ 20,000,000
Proceeds from issuance of notes		$ 193,200,000
Debt instrument, maturity date		Jul. 01, 2028							Jul. 01, 2028	Jul. 01, 2028
Debt instrument, convertible trading days | Days		20
Debt instrument, convertible consecutive trading days | Days		30
Debt instrument, convertible conversion price percentage		130.00%
Debt instrument, convertible principal amount		$ 1,000
Debt instrument, convertible maximum conversion price percentage		98.00%
Debt instrument, conversion initial rate | shares		24.5586
Debt instrument, convertible principal amount		$ 1,000
Debt instrument, conversion price | $ / shares		$ 40.72
Debt instrument, redemption price percentage of principal amount		100.00%
Debt instrument, sinking fund		$ 0
Debt instrument, percentage of repurchase principal amount		100.00%
Long-Term Debt									$ 120,691,000	$ 120,229,000
Debt unamortized issuance costs, net									1,809,000	2,271,000
Debt, principal amount, net									122,500,000
Unamortized issuance costs									1,800,000
1.50% Convertible Senior Notes Due 2028 | Additional Paid-in-Capital
Debt Instrument [Line Items]
Fair value of the embedded conversion feature									4,100,000
1.50% Convertible Senior Notes Due 2028 | Minimum
Debt Instrument [Line Items]
Debt instrument, convertible trading days | Days		20
Debt instrument, convertible conversion price percentage		130.00%
1.50% Convertible Senior Notes Due 2028 | Maximum
Debt Instrument [Line Items]
Debt instrument covenants, percentage of aggregate principal amount payable.		25.00%
3.00% Convertible Senior Notes Due 2025
Debt Instrument [Line Items]
Aggregate principal amount						$ 175,000,000			87,500,000	87,500,000
Debt instrument convertible, if-converted value of the Notes less than its principal amount									$ 160,900,000	$ 83,600,000
Debt instrument, interest rate						3.00%			3.00%	3.00%
Debt Instrument, option to purchase additional principal amount						$ 25,000,000
Proceeds from issuance of notes						$ 169,800,000
Debt instrument, maturity date						Jun. 01, 2025			Jun. 01, 2025	Jun. 01, 2025
Debt instrument, convertible trading days | Days						20
Debt instrument, convertible consecutive trading days | Days						30
Debt instrument, convertible conversion price percentage						130.00%
Debt instrument, convertible principal amount						$ 1,000
Debt instrument, convertible maximum conversion price percentage						98.00%
Debt instrument, conversion initial rate | shares						26.7271
Debt instrument, convertible principal amount						$ 1,000
Debt instrument, conversion price | $ / shares						$ 37.42
Debt instrument, redemption price percentage of principal amount						100.00%
Debt instrument, sinking fund						$ 0
Debt instrument, percentage of repurchase principal amount						100.00%
Debt instrument repurchase amount									$ 87,500,000
Long-Term Debt									87,094,000	$ 86,508,000
Debt unamortized issuance costs, net									406,000	992,000
Debt, principal amount, net									$ 175,000,000
3.00% Convertible Senior Notes Due 2025 | Minimum
Debt Instrument [Line Items]
Debt instrument, convertible trading days | Days						20
Debt instrument, convertible conversion price percentage						130.00%
Conversion feature percentage									10.00%
3.00% Convertible Senior Notes Due 2025 | Maximum
Debt Instrument [Line Items]
Debt instrument covenants, percentage of aggregate principal amount payable.						25.00%
1.50% Convertible Senior Notes Due 2025
Debt Instrument [Line Items]
Aggregate principal amount									$ 87,500,000	$ 87,500,000
Payment on debt issuance costs									$ 14,300,000
Debt instrument, interest rate									1.50%	1.50%
Debt instrument, maturity date									Jul. 01, 2028	Jul. 01, 2028
Long-Term Debt									$ 74,121,000	$ 69,214,000
Debt unamortized issuance costs, net									10,602,000	14,490,000
Payment of refinancing fees to lender									3,800,000
Four Year Senior Secured Term Loan Facility | Senior Credit Facilities
Debt Instrument [Line Items]
Debt instrument term					4 years
Credit facility maximum borrowing capacity					$ 125,000,000.0
Net proceeds from issuance of credit facility					123,000,000.0
Four Year Senior Secured Term Loan Facility | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Debt instrument periodic payments equivalent percentage of annual amount on original principal amount during first two years				1.25%
Debt instrument periodic payments equivalent percentage of annual amount on original principal amount after two years				2.50%
Senior Secured First-lien Revolving Credit Facility | Senior Credit Facilities
Debt Instrument [Line Items]
Aggregate principal amount							$ 24,700,000
Debt repayment cost							106,300,000
Extinguishment of debt							104,900,000
Loss on extinguishment of debt							$ 1,300,000
Credit facility borrowed									0	$ 0
Credit facility maximum borrowing capacity					$ 50,000,000.0
Net Leverage Ratio Greater Than 3.00 | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio				3.00
Unused line fee percentage				50.00%
Net Leverage Ratio Greater Than 3.00 | Amended Senior Credit Facilities | L I B O R
Debt Instrument [Line Items]
Net leverage ratio				3.00
Debt Instrument, basis spread on variable rate				3.00%
Net Leverage Ratio Greater Than 3.00 | Amended Senior Credit Facilities | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate				2.00%
Net Leverage Ratio Greater Than 3.00 | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net leverage ratio			3
Net Leverage Ratio Greater Than 3.00 | Credit Agreement Amendment Two | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			2.00%
Net Leverage Ratio Greater Than 3.00 | Credit Agreement Amendment Two | SOFR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			0.10%
Net Leverage Ratio Greater Than 3.00 | Credit Agreement Amendment Two | SOFR plus Ten Basis Point Credit Spread Member
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			3.00%
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Unused line fee percentage				45.00%
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Amended Senior Credit Facilities | L I B O R
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate				2.75%
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Amended Senior Credit Facilities | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate				1.75%
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Credit Agreement Amendment Two | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			1.75%
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Credit Agreement Amendment Two | SOFR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			0.10%
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Credit Agreement Amendment Two | SOFR plus Ten Basis Point Credit Spread Member
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			2.75%
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Minimum | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio				2.50
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Minimum | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net leverage ratio			2.5
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Maximum | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio				3.00
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Maximum | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net leverage ratio			3
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Unused line fee percentage				40.00%
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Amended Senior Credit Facilities | L I B O R
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate				2.50%
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Amended Senior Credit Facilities | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate				1.50%
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Credit Agreement Amendment Two | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			1.50%
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Credit Agreement Amendment Two | SOFR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			0.10%
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Credit Agreement Amendment Two | SOFR plus Ten Basis Point Credit Spread Member
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			2.50%
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Minimum | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio				2.00
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Minimum | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net leverage ratio			2
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Maximum | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio				2.50
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Maximum | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net leverage ratio			2.5
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Unused line fee percentage				35.00%
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Amended Senior Credit Facilities | L I B O R
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate				2.25%
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Amended Senior Credit Facilities | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate				1.25%
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Credit Agreement Amendment Two | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			1.25%
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Credit Agreement Amendment Two | SOFR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			0.10%
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Credit Agreement Amendment Two | SOFR plus Ten Basis Point Credit Spread Member
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			2.25%
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Minimum | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio				1.50
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Minimum | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net leverage ratio			1.5
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Maximum | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio				2.00
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Maximum | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net leverage ratio			2
Net Leverage Ratio Less Than or Equal to 1.50 | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio				1.50
Unused line fee percentage				30.00%
Net Leverage Ratio Less Than or Equal to 1.50 | Amended Senior Credit Facilities | L I B O R
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate				2.20%
Net Leverage Ratio Less Than or Equal to 1.50 | Amended Senior Credit Facilities | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate				1.00%
Net Leverage Ratio Less Than or Equal to 1.50 | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net leverage ratio			1.5
Net Leverage Ratio Less Than or Equal to 1.50 | Credit Agreement Amendment Two | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			1.00%
Net Leverage Ratio Less Than or Equal to 1.50 | Credit Agreement Amendment Two | SOFR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			0.10%
Net Leverage Ratio Less Than or Equal to 1.50 | Credit Agreement Amendment Two | SOFR plus Ten Basis Point Credit Spread Member
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			2.20%
Modified Notes
Debt Instrument [Line Items]
Long-Term Debt									161,200,000
Debt unamortized issuance costs, net									$ 13,800,000
Period One June 30, 2024 | Credit Agreement Amendment Three
Debt Instrument [Line Items]
Minimum earnings before interest taxes depreciation and amortization	$ 5,000,000
Period Two September 30, 2024 | Credit Agreement Amendment Three
Debt Instrument [Line Items]
Minimum earnings before interest taxes depreciation and amortization	7,500,000
Period Three December 31, 2024 | Credit Agreement Amendment Three
Debt Instrument [Line Items]
Minimum earnings before interest taxes depreciation and amortization	20,000,000
Period Four March 31, 2025 | Credit Agreement Amendment Three
Debt Instrument [Line Items]
Minimum earnings before interest taxes depreciation and amortization	30,000,000
Period Five June 30, 2025 | Credit Agreement Amendment Three
Debt Instrument [Line Items]
Minimum earnings before interest taxes depreciation and amortization	35,000,000
Period Five September 30, 2025 | Credit Agreement Amendment Three
Debt Instrument [Line Items]
Minimum earnings before interest taxes depreciation and amortization	35,000,000
Period Six December 31, 2025 | Credit Agreement Amendment Three
Debt Instrument [Line Items]
Minimum earnings before interest taxes depreciation and amortization	40,000,000
Period Seven March 31, 2026 | Credit Agreement Amendment Three
Debt Instrument [Line Items]
Minimum earnings before interest taxes depreciation and amortization	$ 40,000,000